A379760 Smallest prime that is the sum of 2n+1 cubes of consecutive odd primes.

66347, 15643, 81647, 279397, 1961623, 3701627, 5644601, 2505187, 8016551, 4695947, 9335519, 6819443, 12830327, 35259463, 35278489, 56759723, 39944393, 86442623, 186387137, 95860493, 118647143, 170943137, 118651139, 509399153, 241399309, 381448853, 877324879

Offset: 1

Author

Michel Lagneau, Jan 02 2025

Keywords

• nonn

Examples

			For n=2, the smallest sum of 2*n+1 = 5 cubed consecutive primes which is prime is a(2) = 7^3 + 11^3 + 13^3 + 17^3 + 19^3 = 15643.
		

Links

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

Crossrefs

Cf. A030078 (cube of primes), A082244 (analog for primes), A380319 (analog for square of primes).

Programs

Maple

P3:= map(t -> t^3, select(isprime,[seq(i,i=3..10^5,2)])):
SP3:= ListTools:-PartialSums(P3):
f:= proc(n) local k;
  for k from 1 do if isprime(SP3[k+2*n+1]-SP3[k]) then return SP3[k+2*n+1]-SP3[k] fi od
end proc:
map(f, [$1..50]); # Robert Israel, Feb 02 2025

Mathematica

a[n_] := Block[{k = 1, s}, While[s = Sum[Prime[i]^3, {i, k, k + 2n}]; !PrimeQ[s], k++ ]; s]; Table[a[n], {n, 1, 27}]

PARI

a(n) = my(k=2, s = sum(i=0, 2*n, prime(k+i)^3)); while (!isprime(s), s -= prime(k)^3; k++; s += prime(k+2*n)^3;); s; \\ Michel Marcus, Jan 20 2025