OFFSET
1,1
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
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.
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Jan 01 2024
STATUS
approved