A302087 Numbers k such that k^2+1 and (k+6)^2+1 are both prime.

4, 10, 14, 20, 84, 110, 120, 124, 150, 170, 204, 224, 230, 250, 264, 300, 400, 430, 464, 490, 570, 674, 680, 690, 930, 960, 1004, 1054, 1060, 1140, 1144, 1150, 1314, 1410, 1434, 1550, 1564, 1570, 1580, 1654, 1784, 1870, 1964, 1974, 2050, 2074, 2080, 2120, 2260, 2304, 2314

Offset: 1

Author

Seiichi Manyama, Mar 31 2018

Keywords

• nonn

Links

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

Crossrefs

Cf. A005574, A023201, A096012, A302021.

Programs

Magma

[n: n in [1..2500] | IsPrime(n^2+1) and IsPrime((n+6)^2+1)]; // Vincenzo Librandi, Apr 02 2018

Maple

select(k->isprime(k^2+1) and isprime((k+6)^2+1),[$1..3000]); # Muniru A Asiru, Apr 02 2018

Mathematica

Select[Range[3000], PrimeQ[#^2 + 1] && PrimeQ[(# + 6)^2 + 1]&] (* Vincenzo Librandi, Apr 02 2018 *)

PARI

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

Python

from sympy import isprime
k, klist, A302087_list = 0, [isprime(i**2+1) for i in range(6)], []
while len(A302087_list) < 10000:
    i = isprime((k+6)**2+1)
    if klist[0] and i:
        A302087_list.append(k)
    k += 1
    klist = klist[1:] + [i] # Chai Wah Wu, Apr 01 2018