cp's OEIS Frontend

A161682 Primes that are not of the form x^3 - y^2.

%I A161682 #21 Jun 10 2025 11:18:37
%S A161682 3,5,17,29,31,37,41,43,59,73,97,101,103,113,131,137,149,157,163,173,
%T A161682 179,181,197,211,227,229,241,257,263,269,281,283,311,313,317,331,337,
%U A161682 347,349,353,367,373,379,383,389,397,401,409,419,421,443,449,457,461,467,479,491,509,521,523,541
%N A161682 Primes that are not of the form x^3 - y^2.
%C A161682 The current values are conjectural as they have been reduced from a finite list of values x^3 - y^2 within a search radius x,y < 10000.
%C A161682 Conjecture: The sequence is infinite.
%C A161682 No more solutions with x < 2.2*10^9. - _Daniel Starodubtsev_, Jan 22 2020
%t A161682 (* assuming x < 10^4 *) notOfTheForm[p_] := Do[r = Reduce[ y > 0 && p == x^3 - y^2, {y}, Integers]; If[r =!= False, If[x > xmax, xmax = x; Print["xmax = ", xmax]]; Return[True]], {x, 1, 10^4}] =!= True; xmax = 1; Reap[ Do[ If[ notOfTheForm[p], Print["p = ", p]; Sow[p]], {p, Prime /@ Range[100]}]][[2, 1]] (* _Jean-François Alcover_, Oct 09 2012 *)
%o A161682 (PARI) diffcubesq(n) =
%o A161682 {
%o A161682 local(a,c=0,c2=0,j,k,y);
%o A161682 a=vector(floor(n^2/log(n^2)));
%o A161682 for(j=1,n,
%o A161682 for(k=1,n, y=j^3-k^2; if(ispseudoprime(y), c++; a[c]=y;););
%o A161682 );
%o A161682 a=vecsort(a);
%o A161682 for(j=2,c/2,
%o A161682 if(a[j]!=a[j-1], c2++; print1(a[j]","); if(c2>100,break););
%o A161682 );
%o A161682 }
%Y A161682 Equals A000040 \ A161681.
%K A161682 nonn
%O A161682 1,1
%A A161682 _Cino Hilliard_, Jun 16 2009
%E A161682 Worthless link removed by _R. J. Mathar_, Jul 16 2009
%E A161682 a(28)-a(61) from _Jean-François Alcover_, Oct 09 2012