A216362 Primes of the form 2^(n-1)*n^2-(-1)^n.

2, 7, 37, 127, 401, 1151, 3137, 8191, 51199, 294911, 1605631, 3686401, 209715199, 10485760001, 8131987999031297, 155444555888459777, 139751824747451132596033945601, 3429749540386513119227714380314826357885676055272856607522817

Offset

1,1

Comments

Generated by n: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 25, 43, 47, 85, 187, 188, 206, 275, 292 ...

Primes of the form 2^(n-1)*n^2+(-1)^n are 1153, 44530220924929, ...

Links

Table of n, a(n) for n=1..18.

Example

a(1) = 2 (= 2^(1 - 1)*1^2 - (-1)^1 = 1 + 1),
a(2) = 7 (= 2^(2 - 1)*2^2 - (-1)^2 = 8 - 1),
a(3) = 37 (= 2^(3 - 1)*3^2 - (-1)^3 = 36 + 1),
a(4) = 127 (= 2^(4 - 1)*4^2 - (-1)^4 = 128 - 1),
a(5) = 401 (= 2^(5 - 1)*5^2 - (-1)^5 = 400 + 1),
a(6) = 1151 (= 2^(6 - 1)*6^2 - (-1)^6 = 1152 - 1),
a(7) = 3137 (= 2^(7 - 1)*7^2 - (-1)^7 = 3136 + 1),
a(8) = 8191 (= 2^(8 - 1)*8^2 - (-1)^8 = 8192 - 1).

Mathematica

a={}; For[n = 1, n <= 300, n++, {v = 2^(n-1)*n^2-(-1)^n; If[PrimeQ[v], AppendTo[a, v]]}]; a   [John W. Layman, Sep 06 2012]

Prog

(PARI)
for (n=1, 10^3, t=2^(n-1)*n^2-(-1)^n; if (isprime(t), print1(t, ", ")));
/* Joerg Arndt, Sep 05 2012 */

Crossrefs

Sequence in context: A042465 A041051 A175487 * A002787 A062394 A245902

Adjacent sequences: A216359 A216360 A216361 * A216363 A216364 A216365

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 05 2012

Status

approved