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

Author

Seiichi Manyama, Mar 31 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A005574, A096012, A302087.

Programs

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

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 *)

PARI

isok(k) = isprime(k^2+1) && isprime((k+2)^2+1) && isprime((k+6)^2+1); \\ Altug Alkan, Apr 02 2018

Python

from sympy 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