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