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%I #44 Mar 02 2019 07:45:00
%S 12,90,208,212,234,242,314,366,404,410,416,486,540,590,750,888,908,
%T 1152,1418,1444,1500,1524,1658,1666,1736,1798,1814,1874,1940,1942,
%U 2094,2138,2266,2496,2584,3058,3062,3206,3660,4034,4080,4208,4368,4422,4606,4872
%N Numbers k such that k^4 is a sum of 4 consecutive primes.
%H Robert G. Wilson v, <a href="/A245577/b245577.txt">Table of n, a(n) for n = 1..5100</a> (first 1189 terms from Zak Seidov)
%e 12^4 = 20736 = prime(689) + prime(689 + 1) + prime(689 + 2) + prime(689 + 3) = 5171 + 5179 + 5189 + 5197.
%t 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 *)
%o (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
%Y Cf. A034963, A051395, A206280.
%K nonn
%O 1,1
%A _Zak Seidov_, Nov 29 2014
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