A111131 Least cube greater than its predecessor such that their difference is a prime or a prime multiplied by a power of two.

1, 8, 27, 64, 125, 343, 729, 1000, 1331, 1728, 2744, 3375, 4913, 5832, 8000, 10648, 13824, 15625, 17576, 21952, 24389, 35937, 42875, 50653, 54872, 59319, 68921, 74088, 79507, 103823, 132651, 166375, 175616, 195112, 205379, 300763, 314432

Offset

1,2

Comments

The sequence was conceived as n^3 is the sum of n primes as shown below:

8=1+7, 27=8+19, 64=27+37, 125=64+61, 343=125+2*109, 729=343+2*193, 1000=729+271 ...

Cube roots are 1,2,3,4,5,7,9,10,11,12,14,15,17,18,20,22,24,25,26,...

Links

Table of n, a(n) for n=1..37.

Mathematica

a[1] = 1; a[n_] := a[n] = Block[{c = a[n - 1], j}, k = c^(1/3) + 1; While[j = 1; While[ IntegerQ[(k^3 - c)/j], j *= 2]; ! PrimeQ[2(k^3 - c)/j], k++ ]; k^3]; Table[ a[n], {n, 37}] (* Robert G. Wilson v *)

Crossrefs

See A111103 for another version.

Sequence in context: A352049 A125496 A030289 * A111103 A076969 A179163

Adjacent sequences: A111128 A111129 A111130 * A111132 A111133 A111134

Keyword

nonn

Author

Giovanni Teofilatto, Oct 14 2005

Extensions

Edited and extended by Robert G. Wilson v, Oct 18 2005

Name clarified by Peter Munn, Jun 17 2021

Status

approved