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

1,1

Links

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

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 *)

Prog

(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
(Magma) [n: n in [1..2500] | IsPrime(n^2+1) and IsPrime((n+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

Crossrefs

Cf. A005574, A023201, A096012, A302021.

Sequence in context: A310422 A310423 A114335 * A329103 A099355 A161366

Adjacent sequences: A302084 A302085 A302086 * A302088 A302089 A302090

Keyword

nonn

Author

Seiichi Manyama, Mar 31 2018

Status

approved