login
A111131
Least cube greater than its predecessor such that their difference is a prime or a prime multiplied by a power of two.
1
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,...
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
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