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 A255635 Numbers n such that 1+16n^2, 1+16(n+1)^2 and 1+16(n+2)^2 are prime. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 7 05:53 EST 2023. Contains 367630 sequences. (Running on oeis4.)