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

Author

Zak Seidov, Feb 28 2015

Keywords

• nonn

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

Crossrefs

Cf. A001912, A005574, A255634.

Programs

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

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 *)

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