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
Keywords
Examples
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.
Crossrefs
Cf. A219634.
Programs
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Mathematica
p=1;lst={p};Do[If[PrimeQ[p+n^3],AppendTo[lst,n];p=p+n^3],{n,1,1500}];lst
Comments