[VA] Short & Sweet Math Challenge #25 "San Valentin's Special: Weird Math"

[Gerson W. Barbosa]

(02-19-2021 11:32 PM)Valentin Albillo Wrote:        

Concoction the Sixth: Weird Year

      Both RPL code and the resulting list of the years have been produced (without comments or explanation), but nearly all the questions have been left unanswered, i.e.:

• What is the "simple but highly remarkable (striking, in fact) numeric property" ?
• (a) How many years will be listed in the output ? ,
• (b) What will be the next predicted potentially catastrophic year after 2020 ?,
• (c) Should we be concerned ?

These were being answered, either explicitly or implicitly, in a post-scriptum to post #17 while you were still writing your post. Sorry for the delay.

(02-19-2021 11:32 PM)Valentin Albillo Wrote:        
      Finally, programs written in other than RPL would be welcome for variety and to let readers better understand what the code does and how their RPN calcs (say) would deal with the problem.

As you please, on the HP-75C:

10 OPTION BASE 1
15 DIM P(20),Y(100)
20 INPUT L
25 N=CEIL(3*(4*L/LOG(L)^2)^(1/3))
30 FOR I=1 TO 20
35 READ P
40 P(I)=P*P
45 NEXT I
50 C=0
55 FOR I=1 TO N
60 FOR J=1 TO N+1-I
65 S=0
70 FOR K=J TO I+J-1
75 S=S+P(K)
80 NEXT K
85 IF S<=L THEN C=C+1 @ Y(C)=S    
90 NEXT J
95 NEXT I
100 FOR I=1 TO C-1
105 FOR J=I TO C
110 IF Y(I)>Y(J) THEN T=Y(I) @ Y(I)=Y(J) @ Y(J)=T
115 NEXT J
120 NEXT I
125 FOR I=1 TO C
130 DISP USING 135 ; Y(I);
135 IMAGE 5d
140 NEXT I
145 DISP
150 END
200 DATA 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
,53,59,61,67,71
         
>RUN
?5000
    4    9   13   25   34   38   49   74
   83   87  121  169  170  195  204  208
  289  290  339  361  364  373  377  458
  529  579  628  650  653  662  666  819
  841  890  940  961  989 1014 1023 1027
 1179 1348 1369 1370 1469 1518 1543 1552
 1556 1681 1731 1802 1849 2020 2189 2209
 2310 2330 2331 2359 2384 2393 2397 2692
 2809 2981 3050 3150 3171 3271 3320 3345
 3354 3358 3481 3530 3700 3721 4011 4058
 4061 4350 4489 4519 4640 4689 4714 4723 
 4727 4852 4899
>                               


Best regards,

Gerson.

Edited to fix lack of linguistic precision in the first paragraph