Non-Figurate Numbers

Jay-qu · 07-21-2009

Quote:

Originally Posted by Turtle

nice. i see no blaring errors and accept the proof until otherwise notified. this gives us the authorization we need to simply subtract the set of primes from the non-figurate set as i suggested (well, went ahead & did)

and then we can focus on what's left to try & find some patterns. can you guys re-write your code to do that subtraction of the primes from the non-figurate set on the fly? over......

Thank you Turtle

The prime number detector is an easy addition, I have one that I wrote last year - but first what do you expect to gain from removing the primes?

Jay-qu · 07-21-2009

here it is, sorry for the bad formatting was in a hurry

Code:

modest · 07-21-2009

I also don't see the use in removing the primes. Whatever pattern is there to be found would include the primes—the primes would be part of the pattern that is.

~modest

Turtle · 07-21-2009

hi fellas!

well, my first answer to why is always because i can.

my thinking though, is that since all-about-primes is well established , whereas all-about-non-figurate-numbers is not established, then setting aside the primes to look at what is left may reveal something about the whole that is otherwise obscured. i don't know what i/we will see; that's why i/we are gonna look.

as to your programs, maybe make it a switch to display, or not to display the primes. save the primes in a separate array/file if you want in such a way that we can put them back in the non-figurate set when we need them.

i will get that list copied in my notepad asap and commence to gazing at it. . . . . .

Turtle · 07-21-2009

hold everything. j-q's edited list doesn't agree with modest's first unedited list.

j-q has 147 as non-figurate and non-prime. it is non-prime, but if it's non-figurate then it should be in modest's original list & it's not.

several other similar mismatches between the lists.

somebody has got something wrong, but i don't know which who be it.

modest · 07-21-2009

It's me. Looking at my code:

Code:

for($checknum = 6; $checknum < 1000; $checknum++){
  $found = 0;
  for($n = 2; $n < $checknum and $found == 0; $n++) {
    for($s = 2; $s < $checknum and $found == 0; $s++) {
    if (($n/2)*(($s-2)*$n-$s+4) == $checknum) {$found = 1;}
    }
  }
  if ($found == 0) {print "$checknum, ";}
}

I start n and s at 2... they should be started at 3, yeah? That'll change a lot! Let me change it...

~modest

EDIT ********* ---->

Ok. Sorry 'bout that. This is hopefully correct. I'll update my images with the patterns:

Code:

7, 8, 11, 13, 14, 17, 19, 20, 23, 26, 29, 31, 32, 37, 38, 41, 43, 44, 47, 50, 53
, 56, 59, 61, 62, 67, 68, 71, 73, 74, 77, 79, 80, 83, 86, 89, 97, 98, 101, 103,
104, 107, 109, 110, 113, 116, 119, 122, 127, 128, 131, 134, 137, 139, 140, 143,
146, 149, 151, 152, 157, 158, 161, 163, 164, 167, 170, 173, 179, 181, 182, 187,
188, 191, 193, 194, 197, 199, 200, 203, 206, 209, 211, 212, 218, 221, 223, 224,
227, 229, 230, 233, 236, 239, 241, 242, 248, 251, 254, 257, 263, 266, 269, 271,
272, 277, 278, 281, 283, 284, 290, 293, 296, 299, 302, 307, 308, 311, 313, 314,
317, 319, 320, 323, 326, 329, 331, 332, 337, 338, 347, 349, 350, 353, 356, 359,
362, 367, 368, 371, 373, 374, 377, 379, 380, 383, 386, 389, 391, 392, 397, 398,
401, 404, 407, 409, 410, 413, 416, 419, 421, 422, 431, 433, 434, 437, 439, 440,
443, 446, 449, 452, 457, 458, 461, 463, 464, 467, 470, 473, 476, 479, 482, 487,
488, 491, 493, 494, 497, 499, 500, 503, 509, 517, 518, 521, 523, 524, 527, 530,
533, 536, 539, 541, 542, 547, 548, 551, 554, 557, 563, 566, 569, 571, 572, 577,
578, 581, 583, 584, 587, 589, 593, 599, 601, 602, 607, 608, 611, 613, 614, 617,
619, 620, 623, 626, 629, 631, 632, 638, 641, 643, 644, 647, 649, 650, 653, 656,
659, 661, 662, 667, 668, 673, 674, 677, 683, 686, 689, 691, 692, 698, 701, 704,
707, 709, 710, 713, 716, 719, 722, 727, 728, 731, 733, 734, 737, 739, 740, 743,
746, 749, 751, 752, 757, 758, 761, 767, 769, 770, 773, 776, 779, 787, 788, 791,
794, 797, 799, 800, 803, 806, 809, 811, 812, 817, 818, 821, 823, 824, 827, 829,
830, 839, 842, 851, 853, 854, 857, 859, 860, 863, 866, 869, 872, 877, 878, 881,
883, 884, 887, 890, 893, 896, 899, 901, 902, 907, 908, 911, 913, 914, 917, 919,
920, 923, 926, 929, 937, 938, 941, 943, 944, 947, 950, 953, 956, 959, 962, 967,
968, 971, 974, 977, 979, 980, 983, 986, 989, 991, 992, 997, 998,

~modest

EDIT ********* AGAIN! ---->

wait... that's the same list I had before...

....

modest · 07-21-2009

Ok. I get 147 as figurate at n = 3 s = 50:

F = (n/2)*((s-2)*n-s+4)
147 = (3/2)*((50-2)*3-50+4

~modest

Jay-qu · 07-21-2009

Well 147 wasn't in my original list of numbers.. so something went wrong in the new program.

Here I have fixed it up:

Code:

7,8,11,13,14,17,19,20,23,26,29,31,32,37,38,41,43,44,47,50,53,56,59,61,62,67,68,71,73,74,77,79,80,83
86,89,97,98,101,103,104,107,109,110,113,116,119,122,127,128,131,134,137,139,140,143,146,149,151,
152,157,158,161,163,164,167,170,173,179,181,182,187,188,191,193,194,197,199,200,203,206,209,211,
212,218,221,223,224,227,229,230,233,236,239,241,242,248,251,254,257,263,266,269,271,272,277,278,
281,283,284,290,293,296,299,302,307,308,311,313,314,317,319,320,323,326,329,331,332,337,338,347,
349,350,353,356,359,362,367,368,371,373,374,377,379,380,383,386,389,391,392,397,398,401,404,407,
409,410,413,416,419,421,422,431,433,434,437,439,440,443,446,449,452,457,458,461,463,464,467,470,
473,476,479,482,487,488,491,493,494,497,499,500,503,509,517,518,521,523,524,527,530,533,536,539,
541,542,547,548,551,554,557,563,566,569,571,572,577,578,581,583,584,587,589,593,599,601,602,607,
608,611,613,614,617,619,620,623,626,629,631,632,638,641,643,644,647,649,650,653,656,659,661,662,
667,668,673,674,677,683,686,689,691,692,698,701,704,707,709,710,713,716,719,722,727,728,731,733,
734,737,739,740,743,746,749,751,752,757,758,761,767,769,770,773,776,779,787,788,791,794,797,799,
800,803,806,809,811,812,817,818,821,823,824,827,829,830,839,842,851,853,854,857,859,860,863,866,
869,872,877,878,881,883,884,887,890,893,896,899,901,902,907,908,911,913,914,917,919,920,923,926,
929,937,938,941,943,944,947,950,953,956,959,962,967,968,971,974,977,979,980,983,986,989,991,992,
997,998,

The 147 was my bad as I had stopped s at 50 to save time while testing the prime part of the code.

But this makes me think I may have made another error.. bear with me for a min. The above list was generated from the complement of n,s<100 so could I have let some other figurates slip in? I will go and check

For my algorithm to ensure all figurates are generated (up to 1000) I need to make sure s,n go up to 1000 also. That should do it.

EDIT: I reran the code and fixed the above numbers.

Turtle · 07-21-2009

Quote:

Originally Posted by modest

Ok. I get 147 as figurate at n = 3 s = 50:

F = (n/2)*((s-2)*n-s+4)
147 = (3/2)*((50-2)*3-50+4

~modest

ok.

as an aside, and if i'm not mistaken, this is where Miss Dio-Phantine can get on stage.

if it is the case that you searched your list to find 147, then suppose you had no list and still needed to find if 147, or any given integer, has an integer solution in n & s. like so:
147 = (n/2)*((s-2)*n-s+4) ?

Quote:

Originally Posted by J-Qinator

The 147 was my bad as I had stopped s at 50 to save time while testing the prime part of the code.

But this makes me think I may have made another error.. bear with me for a min. The above list was generated from the complement of n,s<100 so could I have let some other figurates slip in? I will go and check.

roger that. . . . . . . .

Turtle · 07-25-2009

Quote:

Originally Posted by Jay-qu

Well 147 wasn't in my original list of numbers.. so something went wrong in the new program.

Here I have fixed it up:

Code:

7,8,11,13,14,17,19,20,23,26,29,31,32,37,38,41,43,44,47,50,53,56,59,61,62,67,68,71,73,74,77,79,80,83
86,89,97,98,101,103,104,107,109,110,113,116,119,122,127,128,131,134,137,139,140,143,146,149,151,
152,157,158,161,163,164,167,170,173,179,181,182,187,188,191,193,194,197,199,200,203,206,209,211,
212,218,221,223,224,227,229,230,233,236,239,241,242,248,251,254,257,263,266,269,271,272,277,278,
281,283,284,290,293,296,299,302,307,308,311,313,314,317,319,320,323,326,329,331,332,337,338,347,
349,350,353,356,359,362,367,368,371,373,374,377,379,380,383,386,389,391,392,397,398,401,404,407,
409,410,413,416,419,421,422,431,433,434,437,439,440,443,446,449,452,457,458,461,463,464,467,470,
473,476,479,482,487,488,491,493,494,497,499,500,503,509,517,518,521,523,524,527,530,533,536,539,
541,542,547,548,551,554,557,563,566,569,571,572,577,578,581,583,584,587,589,593,599,601,602,607,
608,611,613,614,617,619,620,623,626,629,631,632,638,641,643,644,647,649,650,653,656,659,661,662,
667,668,673,674,677,683,686,689,691,692,698,701,704,707,709,710,713,716,719,722,727,728,731,733,
734,737,739,740,743,746,749,751,752,757,758,761,767,769,770,773,776,779,787,788,791,794,797,799,
800,803,806,809,811,812,817,818,821,823,824,827,829,830,839,842,851,853,854,857,859,860,863,866,
869,872,877,878,881,883,884,887,890,893,896,899,901,902,907,908,911,913,914,917,919,920,923,926,
929,937,938,941,943,944,947,950,953,956,959,962,967,968,971,974,977,979,980,983,986,989,991,992,
997,998,

The 147 was my bad as I had stopped s at 50 to save time while testing the prime part of the code.

But this makes me think I may have made another error.. bear with me for a min. The above list was generated from the complement of n,s<100 so could I have let some other figurates slip in? I will go and check

For my algorithm to ensure all figurates are generated (up to 1000) I need to make sure s,n go up to 1000 also. That should do it.

EDIT: I reran the code and fixed the above numbers.

roger. the fix is in. i can strip out the primes from your corrected list by hand to get my restricted view if the programming you wrote for that is hiccuping. in the mean time, what do you think about my earlier question? >>

Quote:

Originally Posted by Turtle

...suppose you had no list and still needed to find if 147, or any given integer I, has an integer solution in n & s. like so:
I = (n/2)*((s-2)*n-s+4) ?