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

1229, 3041, 3719, 3793, 4969, 5107, 6217, 6317, 6661, 7517, 8807, 8963, 9011, 9883, 10093, 10247, 11311, 12983, 13331, 15443, 17839, 19801, 21149, 21727, 22639, 23417, 23629, 24223, 24709, 25349, 26813, 27329, 27691, 28123, 28711, 28807, 28837, 29453, 29587, 30161, 31327, 32069, 34421, 35267

Offset: 1

Author

Robert Israel, Jan 01 2024

Keywords

• nonn

Comments

Primes p such that A001222(A133525(A000720(p))) = 2.

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000720, A001222, A133525.

Programs

Maple

N:= 10000: # for terms up to prime(N)
P:= [seq(ithprime(i),i=1..N+3)]:
P3:= map(`^`,[0,op(P)],3):
S:= ListTools:-PartialSums(P3):
R:= [seq](S[i+4]-S[i],i=1..N):
P[select(i -> isprime(R[i]/2), [$3..N])];

Mathematica

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];
lst[44] (* Robert P. P. McKone, Jan 02 2024 *)