OEIS featured in The New York Times

05212023, 11:44 PM
Post: #1




OEIS featured in The New York Times
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Hi, all, Today (Sunday, May 21th, 2023) The New York Times features an article commemorating OEIS (OnLine Encyclopedia of Integer Sequences) 50th anniversary: What Number Comes Next? The Encyclopedia of Integer Sequences Knows It makes for a good read and it's nice to see a math website being featured in a main USA newspaper. Have a look at a sequence mentioned in the article, namely:
10 DESTROY ALL @ STD @ N=1 @ P=1 20 LOOP @ DISP N; @ IF NOT MOD(N,2) THEN N=N DIV 2 ELSE P=FPRIM(P+1) @ N=N+P 30 END LOOP >RUN
V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

05222023, 12:21 AM
Post: #2




RE: OEIS featured in The New York Times
(05212023 11:44 PM)Valentin Albillo Wrote: 20 LOOP @ DISP N; @ IF NOT MOD(N,2) THEN N=N DIV 2 ELSE P=FPRIM(P+1) @ N=N+P Cool! Unfortunately, my memories of the 71B are rapidly fading with age. Is FPRIM builtin, or is it in the Math ROM, or in the JPC ROM, or something else? Thanks for refreshing my memory. <0ɸ0> Joe 

05222023, 12:56 AM
Post: #3




RE: OEIS featured in The New York Times
(05222023 12:21 AM)Joe Horn Wrote:(05212023 11:44 PM)Valentin Albillo Wrote: 20 LOOP @ DISP N; @ IF NOT MOD(N,2) THEN N=N DIV 2 ELSE P=FPRIM(P+1) @ N=N+P You're welcome. FPRIM is in the fantastic JPC ROM, as are LOOP and END LOOP. Best regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

05302023, 03:40 PM
Post: #4




RE: OEIS featured in The New York Times
This recent post from Valentín seems to have gone unfairly unnoticed. It's not one of his great challenges, but it's still an interesting topic to the calculatorminded or mathematicallyminded folk that hang out in this forum, I believe.
While I was not able to read the NYT article, which is blocked to nonsubscribers, I've been exploring the OEIS site which was new to me. It's quite a source of interesting and fun stuff! It would have been fantastic to have OEIS during the heyday of the HP calcs, when we were looking for any idea we could transform into a program in our beloved little toys. Thanks, Valentín, for posting this entertaining and informative thread! 

05302023, 06:05 PM
Post: #5




RE: OEIS featured in The New York Times
I always enjoy Valentin's posts, so not I'm not certain how I missed this one.
I've been aware of OEIS for some time, mainly because of Mathematica and Maple listings, but it was nice to see Valentin's approach to that particular number sequence using the 71B. There's always something new to learn with the manner in which Valentin approaches things. Not that I've kept his program listing for adding them the missing trigonometric functions on any of my 12C's, I was totally transfixed whilst studying the listing. I hadn't seen the NYT piece either. I used to get access via my Apple One subscription, but the NYT pulled out a few years back. Living in the UK and being a lifetime reader (and subscriber for most of it) of The Guardian, I wasn't going to pay the NYT directly for the privilege! The Washington Post has always been more my US newspaper taste anyway. On a separate note, concerning the JPC ROM. I've been tempted to download the compendiums of Paris Chapter 48 programs that Eric publishes on hpcalc.org. But there's no handy index (like the one for Joe's Goodies), so it would involve an awful lot of manual sifting. Does anyone know if there's anything worth investigating within the various discs that isn't already published on the rest of hpcalc.org? No worries if not, it's just that I've read great things about the Paris chapter over the years. 

05302023, 06:25 PM
Post: #6




RE: OEIS featured in The New York Times
(05302023 06:05 PM)jonmoore Wrote: On a separate note, concerning the JPC ROM. I've been tempted to download the compendiums of Paris Chapter 48 programs that Eric publishes on hpcalc.org. What are you referring to, exactly? I can't find anything about the JPC ROM or the PPC Paris Chapter on hpcalc.org. JF 

05302023, 07:19 PM
(This post was last modified: 05302023 07:23 PM by jonmoore.)
Post: #7




RE: OEIS featured in The New York Times
(05302023 06:25 PM)JF Garnier Wrote:(05302023 06:05 PM)jonmoore Wrote: On a separate note, concerning the JPC ROM. I've been tempted to download the compendiums of Paris Chapter 48 programs that Eric publishes on hpcalc.org. The JPC ROM is for the 71B and I first encountered it here: http://www.jeffcalc.hp41.eu/emu71/jpcrom.html When I saw it mentioned in this thread, it acted as an aidemémoire ref the PPCParis User Club. For the HP historians, this is a great read  it's a link within the above page, but it's easy to miss: http://www.jeffcalc.hp41.eu/emu71/files/jpcromstory.pdf 

05302023, 07:48 PM
Post: #8




RE: OEIS featured in The New York Times
(05302023 07:19 PM)jonmoore Wrote:(05302023 06:25 PM)JF Garnier Wrote: What are you referring to, exactly? So, only fair to warn you that the person who created that website is the person you are answering... Bob Prosperi 

05302023, 08:07 PM
Post: #9




RE: OEIS featured in The New York Times  
06022023, 01:09 AM
Post: #10




RE: OEIS featured in The New York Times
Hi again, Thanks a lot to Fernando del Rey and jonmoore for their interest and very kind words, much appreciated. Re the OEIS (OnLine Encyclopedia of Integer Sequences), I heartily recommend reading these PDF documents to all people new to it:
The OnLine Encyclopedia of Integer Sequences  An illustrated guide with many unsolved problems (37page PDF) A Handbook of Integer Sequences  Fifty Years Later (23page PDF) I Wrote:[...] Generating the sequence is trivial [...] Indeed there is, and presently I'll mention a couple. First of all, the sequence is conjectured to include all positive integers 1, 2, 3, ..., as elements, and we can investigate this alleged fact by using this 5liner for the HP71B, which takes as input K, the maximum number of elements to generate, and will output the pairs (number, index) for up to the first 60 numbers (1..60), where index is the lowest one where number first appears in the sequence. It will also output how many numbers weren't found within the first K elements (plus timing) and finally it will explicitly list all numbers not found:
20 FOR C=1 TO K @ IF N>K THEN STD ELSE IF NOT D(N) THEN D(N)=C 30 IF MOD(N,2) THEN P=FPRIM(P+1) @ N=N+P ELSE N=N DIV 2 40 NEXT C @ C=0 @ FOR I=1 TO MIN(K,60) @ IF D(I) THEN DISP (I,D(I)); ELSE C=C+1 @ M(C)=I 50 NEXT I @ DISP @ DISP "Not found:";C;TIME$ @ FOR I=1 TO C @ DISP M(I); @ NEXT I @ DISP
Not found: 21 (timing) 13 17 19 25 26 27 32 33 34 36 38 41 47 49 50 52 54 56 57 59 60 Of course, increasing the maximum number of elements to explore will probably result in finally locating the first occurrence of some or all the numbers not found within the first 100 elements of the sequence. Indeed, running the above program for 100, 200, ...., 2000 elements we get these results:
 100 21 13 17 19 25 26 27 32 33 34 36 38 41 47 49 50 52 54 56 57 59 60 200 12 13 25 26 27 32 36 41 49 50 52 54 60 500 8 25 27 32 36 49 50 54 60 1000 6 25 27 36 50 54 60 2000 4 27 36 54 60 Now we can try to locate the first occurrence of the 4 missing numbers (27, 36, 54, 60) in a faster way and using minimal memory by running this 4line HP71B program, which will accept the number to locate and will search for it among the first 1,000,000 elements (if not using a very fast emulator, you might want to reduce this upper limit to save time; generating a million elements requires primes up to 4,761,697):
20 FOR C=1 TO 1000000 @ IF N=K THEN DISP N;C;TIME$ @ END 30 IF MOD(N,2) THEN P=FPRIM(P+1) @ N=N+P ELSE N=N DIV 2 40 NEXT C @ DISP "Not found: ";TIME$
? 25 > 25 1154 (timing)
? 27 > 27 161336 (Emu71/Win @972x: 28", go71b @128x: 3'36", Physical: 7h 41') ? 60 > 60 614667 (Emu71/Win @972x: 3'3", go71b @128x: 23'14", Physical: ~ 50h) Unfortunately, the search up to index 1,000,000 fails for 36 because its first occurrence in the sequence happens to be at index 77,534,485,877 !!. Even worse, if considering numbers up to 100 instead of up to 60, the number 97 first appears at index 17,282,073,747,557 !!! Additionally, a second conjecture is that every positive integer appears in the sequence not just once but an infinite number of times. We can check it out by finding multiple indexes for any given input number, simply delete the END statement at line 20 and reduce to 100,000 the maximum index to search up to. Line 20 will then look like this:
? 1 > 1 8 12 20 742 ... (the very next appearance is at index 513,152,128) ? 2 > 7 11 19 741 ... (ditto at index 513,152,127) ? 3 > 2 4 15 46 95 6355 ... ? 5 > 71 4849 ... (no others up to index 1,000,000) ? 7 > 25 114 123 446 7104 ... ? 13 > 345 418 4621 ... (no others up to index 1,000,000) ? 25 > 1154 1519 10359 13330 ... (no others up to index 1,000,000) ? 85 > 140 3161 72349... Additional Trivia: ● A few other nice appearances are 31416 at indexes 6,768 and 6,923, 11111 at 12,497, 55555 at 56,551, 100000 at 26,488 and last but not least, 2023 at 2,165. On the other hand, 1992 does not appear within the first 1,000,000 elements. ● There's a number of solutions of A(n) = n, i.e. numbers whose index in the sequence equals the number itself. They can be found very easily with a trivial modification of my second program above, and the first ones are n = 1, 16, 787, 427447 and no others up to index 1,000,000. Regards. V. All My Articles & other Materials here: Valentin Albillo's HP Collection 

07232024, 07:59 AM
Post: #11




RE: OEIS featured in The New York Times
New York Times featuring the OEIS is a testament to the profound impact of mathematical sequences on various fields. It highlights how the exploration of patterns and numbers can inspire new insights and innovations.
spelling bee answers 

07242024, 09:08 AM
(This post was last modified: 07242024 09:21 AM by Gil.)
Post: #12




RE: OEIS featured in The New York Times
Just a possible, simple adaptation for the HP50G calculator:
Code: \<< DUP 1 1 \> n l p As argument, enter the number n for the the number of elements to be calculated. But in fact, no necessity to save the last element calculated, we can just play on its duplication. The above program becomes then: Code: \<< DUP 1 \> n p 

07252024, 08:32 PM
Post: #13




RE: OEIS featured in The New York Times
(07242024 09:08 AM)Gil Wrote: But in fact, no necessity to save the last element calculated, we can just play on its duplication. The above program becomes then: Nice program, simple and fast. Here is a slightly modified version to illustrate a couple of memory saving tips. This is not meant as criticism of your program, just as information that may be of help to you and others. Code:
My first tip turns out not to save any memory in this case but deserves mention. I have always heard that in IF..THEN..(ELSE)..END structures, having exactly one object between IF and ELSE minimizes memory use. It seems that your method of having nothing between IF and ELSE uses no more memory. I do think that my version is more readable but that may not be the case with other programs. My next tip is to use 2 n START rather than 1 n 1  START which does the same number of iterations but saves 5 bytes. Note that this may not work with FOR loops where the value of the looping variable would be different, but is always safe to use with START loops. A final, simple tip is to use the extended stack operations available on the HP 49 and 50. In this case I replaced DUP DUP with DUPDUP, saving 2.5 bytes. Others include UNROT, PICK3 and NIP. These extended stack operations are faster than their equivalents, as well as saving memory. 

07252024, 11:35 PM
Post: #14




RE: OEIS featured in The New York Times
Thanks for the tips, John, above all regarding the cleaner & more logical 2 n START... NEXT, that, besides memory saving, for 1 million loops/start seems — logically — to reduce the execution time by a factor of 1.001 in comparison to 1 n 1  START... NEXT.
IF "condition" THEN... ELSE... is, yes, clearer than "condition" IF THEN... ELSE: an habit from RPN logic. DUP DUP is just safer — to include potential users of the old HP48 that can't use the new, faster command DUPDUP. 

07252024, 11:59 PM
(This post was last modified: 07262024 12:03 AM by Gil.)
Post: #15




RE: OEIS featured in The New York Times
By the way, it seems on HP50G/EMU48 that putting the condition/result before the IF THEN END is faster for the following program:
Code: \<< than putting the condition/result just after the IF as here: Code: \<< 

07262024, 11:57 AM
Post: #16




RE: OEIS featured in The New York Times
(07252024 11:59 PM)Gil Wrote: By the way, it seems on HP50G/EMU48 that putting the condition/result before the IF THEN END is faster ... Testing on my physical 50g and EMU48, the difference is slight, less than 0.5%. However, Code: \<< using approximate numbers, is 8 times as fast. Of course, not all programs can use approximate numbers but if the numbers are < 10^12 and exact integers are not required, the time savings can be significant. By the way, the decimal points following integers do not cause problems with the HP48, they are simply ignored. Finally, apologies to Valentin for derailing his thread on the OEIS (of which I am a huge fan) with discussions of his least favorite programming language. 

07262024, 06:07 PM
Post: #17




RE: OEIS featured in The New York Times
My apologises too to Valentin.
Regards, Gil 

07272024, 07:25 PM
(This post was last modified: 07272024 07:51 PM by C.Ret.)
Post: #18




RE: OEIS featured in The New York Times
Bonjour à toutes et à tous.
I would like to intervene on behalf of Gil and John. Even though their discussion regarding the use this really esoteric language has made a small digression; their interventions allowed me to notice this very interesting subject that I had not seen last year. Determining The Sisyphus sequence seems easy with a machine equipped with a JPCROM that, like other specific pocket computers, allows you to easily have the prime numbers in sequence. But what about a machine without this very opportunistic feature? This is the question I asked myself and to try to explore the possible methods, I took my SHARP PC1211 out of its hard case. The first program proposed by Valentin led me to this adaptation: 1: D=4.2424626 , W=10Ǣ7 , N=1 , P=1 2: PRINT N : N=N/2 : IF N>INT N GOSUB 5 : N=2N+P 3: GOTO 2 5: IF P<7 LET P=1+P+(P>2 : RETURN 6: P=P+INT D , D=10DW*INT D , F=5 7: F=F+2 , Q=P/F : IF Q<F RETURN 8: GOTO 6+(Q>INT Q where Ǣ stand for the Exp key (10exponentiation key) As the SHARP PC1211 is not fast, I tried to optimize things by determining the next prime number from a rudimentary generator of quasiprime numbers. In reality, integers that are not multiples of 2, 3 or 5. Which facilitates primality tests based on divisibility by odd factors, thus starting only from 7. My code seems to work and list the integers of the sequence quite quickly (for this SHARP). But I have trouble finding an efficient method to adapt the codes given by Valentin later. In particular, how to find with a PC1211 the results obtained by an HP71B without having to wait a century? Any ideas or suggestions are of course welcome 

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