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A368637 Primes p such that the sum of cubes of the 4 consecutive primes starting with p is twice a prime.

%I A368637 #8 Jan 12 2024 22:46:36
%S A368637 1229,3041,3719,3793,4969,5107,6217,6317,6661,7517,8807,8963,9011,
%T A368637 9883,10093,10247,11311,12983,13331,15443,17839,19801,21149,21727,
%U A368637 22639,23417,23629,24223,24709,25349,26813,27329,27691,28123,28711,28807,28837,29453,29587,30161,31327,32069,34421,35267
%N A368637 Primes p such that the sum of cubes of the 4 consecutive primes starting with p is twice a prime.
%C A368637 Primes p such that A001222(A133525(A000720(p))) = 2.
%H A368637 Robert Israel, <a href="/A368637/b368637.txt">Table of n, a(n) for n = 1..10000</a>
%e A368637 a(3) = 3719 is a term because 3719, 3727, 3733, 3739 are 4 consecutive primes with 3719^3 + 3727^3 + 3733^3 + 3739^3 = 2 * 103749725899 with 103749725899 prime.
%p A368637 N:= 10000: # for terms up to prime(N)
%p A368637 P:= [seq(ithprime(i),i=1..N+3)]:
%p A368637 P3:= map(`^`,[0,op(P)],3):
%p A368637 S:= ListTools:-PartialSums(P3):
%p A368637 R:= [seq](S[i+4]-S[i],i=1..N):
%p A368637 P[select(i -> isprime(R[i]/2), [$3..N])];
%t A368637 lst[maxN_] := Module[{p = 2, i = 1, l = {}}, Monitor[While[i <= maxN, If[PrimeQ[Total[Take[Prime[Range[PrimePi[p], PrimePi[p] + 3]], 4]^3]/2], AppendTo[l, p]; i++; ]; p = NextPrime[p]; ], i]; l];
%t A368637 lst[44] (* _Robert P. P. McKone_, Jan 02 2024 *)
%Y A368637 Cf. A000720, A001222, A133525.
%K A368637 nonn
%O A368637 1,1
%A A368637 _Robert Israel_, Jan 01 2024