A219635 a(n) is the smallest number > a(n-1) such that 1 + a(1)^3 + a(2)^3 + ... + a(n)^3 is a prime.

1, 3, 8, 12, 18, 22, 24, 36, 44, 52, 60, 66, 74, 102, 112, 116, 124, 134, 136, 156, 224, 234, 246, 304, 312, 320, 340, 374, 390, 396, 402, 426, 450, 460, 522, 528, 554, 568, 588, 612, 632, 640, 654, 660, 686, 700, 704, 706, 710, 718, 762, 764, 772, 788, 846

Offset

1,2

Comments

The corresponding primes are 2, 29, 541, 2269, 8101, 18749, 32573,...

Links

Table of n, a(n) for n=1..55.

Example

a(1) = 1 because 1 + 1^3 = 2 is prime;
a(2) = 3 because 1 + 1^3 + 2^3 = 10 is not prime, but 1 + 1^3 + 3^3 = 29 is prime;
a(3) = 8 because 1 + 1^3 + 3^3 + 4^3 = 93, 1 + 1^3 + 3^3 + 5^3 = 154, 1 + 1^3 + 3^3 + 6^3 = 245, and 1 + 1^3 + 3^3 + 7^3 = 372 are all nonprime, but 1 + 1^3 + 3^3 + 8^3 = 541 is prime.

Mathematica

p=1; lst={p}; Do[If[PrimeQ[p+n^3], AppendTo[lst, n]; p=p+n^3], {n, 1, 1500}]; lst

Crossrefs

Cf. A219634.

Sequence in context: A189758 A190368 A256711 * A063225 A213238 A005660

Adjacent sequences: A219632 A219633 A219634 * A219636 A219637 A219638

Keyword

nonn

Author

Michel Lagneau, Nov 24 2012

Status

approved