The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A161681 Primes that are the difference between a cube and a square (conjectured values). 3
 2, 7, 11, 13, 19, 23, 47, 53, 61, 67, 71, 79, 83, 89, 107, 109, 127, 139, 151, 167, 191, 193, 199, 223, 233, 239, 251, 271, 277, 293, 307, 359, 431, 433, 439, 463, 487, 499, 503, 547, 557, 587, 593, 599, 631, 647, 673, 683, 719, 727, 769, 797, 859, 887, 919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The primes found among the differences are sorted in ascending order and unique primes are then extracted. I call this a "conjectured" sequence since I cannot prove that somewhere on the road to infinity there will never exist an integer pair x,y such that x^3-y^2 = 3,5,17,..., missing prime. For example, testing x^3-y^2 for x,y up to 10000, the count of some duplicates are: duplicate,count 7,2 11,2 47,3 431,7 503,7 1999,5 28279,11 Yet for 3,5,17,29,... I did not find even one. [Comment from Charles R Greathouse IV, Nov 03 2009: 587 = 783^3 - 21910^2, 769 = 1025^3 - 32816^2, and 971 = 1295^3 - 46602^2 were skipped in the original.] Conjecture: The number of primes in x^3-y*2 is infinite. Conjecture: The number of duplicates for a given prime is finite. Then there is the other side - the primes that are not in the sequence 3, 5, 17, 29, 31, 37, 41, 43, 59, 73, 97, 101, 103, ... Looks like a lot of twin components here. Do these have an analytical form? Is there such a thing as a undecidable sequence? Range of A167224. - Reinhard Zumkeller, Oct 31 2009 LINKS R. Zumkeller, Some Examples [From Reinhard Zumkeller, Oct 31 2009] FORMULA Integers x,y such that x^3-y^2 = p where p is prime. The generation bound is 10000. EXAMPLE 3^3 - 4^2 = 15^3 - 58^2 = 11. PROG (PARI) diffcubesq(n) = {   local(a, c=0, c2=0, j, k, y);   a=vector(floor(n^2/log(n^2)));   for(j=1, n,     for(k=1, n,       y=j^3-k^2;       if(ispseudoprime(y),         c++;         a[c]=y;       )     )   );   a=vecsort(a);   for(j=2, c/2,     if(a[j]!=a[j-1],       c2++;       print1(a[j]", ");       if(c2>100, break);     )   ); } CROSSREFS Cf. A000040. Sequence in context: A138889 A097143 A038897 * A020583 A140557 A027697 Adjacent sequences:  A161678 A161679 A161680 * A161682 A161683 A161684 KEYWORD nonn AUTHOR Cino Hilliard, Jun 16 2009 EXTENSIONS Extended and edited by Charles R Greathouse IV, Nov 03 2009 Further edits by N. J. A. Sloane, Nov 09 2009 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)