OEIS featured in The New York Times
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05-21-2023, 11:44 PM
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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 (On-Line 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 |
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05-22-2023, 12:21 AM
Post: #2
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RE: OEIS featured in The New York Times
(05-21-2023 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 built-in, or is it in the Math ROM, or in the JPC ROM, or something else? Thanks for refreshing my memory. <0|ɸ|0> -Joe- |
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05-22-2023, 12:56 AM
Post: #3
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RE: OEIS featured in The New York Times
(05-22-2023 12:21 AM)Joe Horn Wrote:(05-21-2023 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 |
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05-30-2023, 03:40 PM
Post: #4
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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 calculator-minded or mathematically-minded folk that hang out in this forum, I believe.
While I was not able to read the NYT article, which is blocked to non-subscribers, 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! |
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05-30-2023, 06:05 PM
Post: #5
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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. |
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05-30-2023, 06:25 PM
Post: #6
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RE: OEIS featured in The New York Times
(05-30-2023 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. J-F |
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05-30-2023, 07:19 PM
(This post was last modified: 05-30-2023 07:23 PM by jonmoore.)
Post: #7
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RE: OEIS featured in The New York Times
(05-30-2023 06:25 PM)J-F Garnier Wrote:(05-30-2023 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 aide-mémoire ref the PPC-Paris 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 |
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05-30-2023, 07:48 PM
Post: #8
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RE: OEIS featured in The New York Times
(05-30-2023 07:19 PM)jonmoore Wrote:(05-30-2023 06:25 PM)J-F 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 |
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05-30-2023, 08:07 PM
Post: #9
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RE: OEIS featured in The New York Times | |||
06-02-2023, 01:09 AM
Post: #10
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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 (On-Line Encyclopedia of Integer Sequences), I heartily recommend reading these PDF documents to all people new to it:
The On-Line Encyclopedia of Integer Sequences - An illustrated guide with many unsolved problems (37-page PDF) A Handbook of Integer Sequences - Fifty Years Later (23-page 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 5-liner for the HP-71B, 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 4-line HP-71B 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 |
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