A245577 Numbers k such that k^4 is a sum of 4 consecutive primes.

12, 90, 208, 212, 234, 242, 314, 366, 404, 410, 416, 486, 540, 590, 750, 888, 908, 1152, 1418, 1444, 1500, 1524, 1658, 1666, 1736, 1798, 1814, 1874, 1940, 1942, 2094, 2138, 2266, 2496, 2584, 3058, 3062, 3206, 3660, 4034, 4080, 4208, 4368, 4422, 4606, 4872

Offset: 1

Author

Zak Seidov, Nov 29 2014

Keywords

• nonn

Examples

			12^4 = 20736 = prime(689) + prime(689 + 1) + prime(689 + 2) + prime(689 + 3) = 5171 + 5179 + 5189 + 5197.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..5100 (first 1189 terms from Zak Seidov)

Crossrefs

Cf. A034963, A051395, A206280.

Programs

Mathematica

fQ[n_] := MemberQ[ Total@# & /@ Partition[ Table[ NextPrime[n^4/4, i], {i, {-3, -2, -1, 1, 2, 3}}], 4, 1], n^4]; Select[ Range@ 5000, fQ] (* Robert G. Wilson v, Dec 03 2014 *)

PARI

isscpn(n) = {np = n^4; p = precprime(np\4); for (i=1, 3, p = precprime(p-1);); while(1, q = nextprime(p+1); r = nextprime(q+1); s = nextprime(r+1); if ((v=p+q+r+s) == np, return (1)); if (v > np, return (0)); p = q;);} \\ Michel Marcus, Nov 30 2014