A161681 -id:A161681 - cp's OEIS frontend

A167224 Table of primes of the form n^3 - k^2, 0<=k<=A077121(n).

7, 23, 11, 2, 109, 89, 61, 191, 167, 47, 307, 199, 19, 503, 487, 463, 431, 223, 151, 71, 53, 991, 919, 271, 1327, 1231, 1187, 547, 431, 307, 1607, 1559, 1439, 1367, 1103, 887, 503, 359, 47, 2161, 2053, 1873, 1621, 1297, 433, 2719, 2663, 2383, 1783, 1223, 1063

Offset: 1

Reinhard Zumkeller, Oct 31 2009

Primes in A167222;

A161681 is the range of this table.

			7;23,11,2;;109,89,61;191,167,47;307,199,19;503,487,... .

R. Zumkeller, Table of n, a(n) for n = 1..10000
R. Zumkeller, Some Examples

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

Original entry on oeis.org

3, 5, 17, 29, 31, 37, 41, 43, 59, 73, 97, 101, 103, 113, 131, 137, 149, 157, 163, 173, 179, 181, 197, 211, 227, 229, 241, 257, 263, 269, 281, 283, 311, 313, 317, 331, 337, 347, 349, 353, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 443, 449, 457, 461, 467, 479, 491, 509, 521, 523, 541

Offset: 1

Cino Hilliard, Jun 16 2009

nonn

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.
Conjecture: The sequence is infinite.
No more solutions with x < 2.2*10^9. - Daniel Starodubtsev, Jan 22 2020

Equals A000040 \ A161681.

(* 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 *)

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););
);
}

Worthless link removed by R. J. Mathar, Jul 16 2009

a(28)-a(61) from Jean-François Alcover, Oct 09 2012

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A167224 Table of primes of the form n^3 - k^2, 0<=k<=A077121(n).

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

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