A302021 Numbers k such that k^2+1, (k+2)^2+1 and (k+6)^2+1 are prime.

4, 14, 124, 204, 464, 1144, 1314, 1564, 1964, 2454, 3134, 4174, 4364, 5584, 5874, 6234, 7804, 8174, 8784, 9874, 9894, 10424, 12354, 12484, 12874, 14034, 14194, 15674, 16224, 18274, 18994, 21134, 21344, 22344, 22624, 23134, 23784, 23944, 24974, 25554, 26504, 26934, 27064, 27804, 29364

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (n = 1..200 from Seiichi Manyama)

Maple

select(k->isprime(k^2+1) and isprime((k+2)^2+1) and isprime((k+6)^2+1), [$1..40000]); # Muniru A Asiru, Apr 02 2018

Mathematica

Select[Range[1, 30000], PrimeQ[#^2 + 1] && PrimeQ[(# + 2)^2 + 1] && PrimeQ[(# + 6)^2 + 1] &] (* Vincenzo Librandi, Apr 02 2018 *)

Prog

(Python)
from python import isprime
k, klist, A302021_list = 0, [isprime(i**2+1) for i in range(6)], []
while len(A302021_list) < 10000:
    i = isprime((k+6)**2+1)
    if klist[0] and klist[2] and i:
        A302021_list.append(k)
    k += 1
    klist = klist[1:] + [i] # Chai Wah Wu, Apr 01 2018
(Magma) [n: n in [1..30000] | IsPrime(n^2+1) and IsPrime((n+2)^2+1) and IsPrime((n+6)^2+1)]; // Vincenzo Librandi, Apr 02 2018
(PARI) isok(k) = isprime(k^2+1) && isprime((k+2)^2+1) && isprime((k+6)^2+1); \\ Altug Alkan, Apr 02 2018

Crossrefs

Cf. A005574, A096012, A302087.

Sequence in context: A240273 A137048 A137056 * A006824 A333730 A344201

Adjacent sequences: A302018 A302019 A302020 * A302022 A302023 A302024

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2018

Status

approved