A255635 Numbers n such that 1+16n^2, 1+16(n+1)^2 and 1+16(n+2)^2 are prime.

4, 29, 44, 64, 109, 174, 329, 614, 1044, 1694, 1879, 2044, 2254, 2474, 2709, 3814, 5024, 5039, 5154, 5364, 5634, 5784, 6244, 6624, 6779, 6804, 6949, 7964, 8079, 8509, 8624, 9034, 9324, 9394, 9729, 10719, 11114, 11504, 11954, 12149, 13064, 13319, 13354, 13554, 14019

Offset

1,1

Comments

Numbers n, n+1 and n+2 are terms in A255634.

The corresponding primes for 1+16n^2 are 257, 13457, 30977, 65537, 190097, 484417, ... (all == 7 mod 10);

The corresponding primes for 1+16(n+1)^2 are 401, 14401, 32401, 67601, 193601, 490001, ... (all == 1 mod 10);

The corresponding primes for 1+16(n+2)^2 are 577, 15377, 33857, 69697, 197137, 495617, ... (all == 7 mod 10).

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Maple

A255635:=n->`if`(isprime(1+16*n^2) and isprime(1+16*(n+1)^2) and isprime(1+16*(n+2)^2), n, NULL): seq(A255635(n), n=1..2*10^4); # Wesley Ivan Hurt, Feb 28 2015

Mathematica

Select[Range[15000], AllTrue[{16#^2, 16(#+1)^2, 16(#+2)^2}+1, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 09 2015 *)

Prog

(PARI) select(n->isprime(1+16*n^2) && isprime(1+16*(n+1)^2) && isprime(1+16*(n+2)^2), vector(15000, n, n)) \\ Colin Barker, Mar 01 2015
(Magma) [n: n in [0..15000] | forall{16*n^2+i: i in [1, 32*n+17, 64*n+65] |  IsPrime(16*n^2+i)}]; // Vincenzo Librandi, Mar 04 2015

Crossrefs

Cf. A001912, A005574, A255634.

Sequence in context: A247278 A278823 A042597 * A280854 A042379 A184301

Adjacent sequences: A255632 A255633 A255634 * A255636 A255637 A255638

Keyword

nonn

Author

Zak Seidov, Feb 28 2015

Status

approved