A255229 Integers n such that n^2 - 1 is the difference of the squares of twin primes.

5, 7, 11, 13, 17, 31, 41, 43, 49, 77, 83, 101, 109, 119, 133, 179, 203, 263, 277, 283, 307, 311, 329, 353, 377, 407, 413, 419, 431, 437, 463, 473, 493, 577, 581, 619, 629, 703, 757, 791, 811, 907, 911, 913, 991, 1001, 1037, 1061, 1103, 1121, 1249, 1289, 1337, 1373, 1441, 1457, 1487, 1523, 1597, 1651, 1781

Offset: 1

Author

Neri Gionata, Feb 18 2015

Keywords

• nonn

Examples

			31^2 - 1 = 241^2 - 239^2, and (239, 241) is a twin prime pair, so 31 is in the sequence.
		

Crossrefs

Cf. A088486 (corresponding lesser twin primes), A111046.

Programs

Mathematica

lst={};f[n_]:=Sqrt[Prime[n]^2-NextPrime[Prime[n],-1]^2+1];
Do[If[Prime[n]-NextPrime[Prime[n],-1]==2&&IntegerQ[f[n]],AppendTo[lst,f[n]]],{n,3,10^5}];lst (* Ivan N. Ianakiev, Mar 30 2015 *)

PARI

lista(nn) = {forprime(p=3, nn, q = precprime(p-1); if (((p-q) == 2) && issquare(d=p^2-q^2+1), print1(sqrtint(d), ", ")); ); } \\ Michel Marcus, Feb 18 2015