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

1,1

Links

Table of n, a(n) for n=1..61.

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A371566 A227576 A114262 * A230217 A317250 A007529

Adjacent sequences: A255226 A255227 A255228 * A255230 A255231 A255232

Keyword

nonn

Author

Neri Gionata, Feb 18 2015

Status

approved