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

1,1

Links

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

Example

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.

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}]

Prog

(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

Crossrefs

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

Sequence in context: A251333 A157620 A174757 * A164129 A043591 A022256

Adjacent sequences: A379756 A379758 A379759 * A379761 A379762 A379763

Keyword

nonn

Author

Michel Lagneau, Jan 02 2025

Status

approved