|
%I #13 Jun 24 2021 02:02:41
%S 1,8,27,64,125,343,729,1000,1331,1728,2744,3375,4913,5832,8000,10648,
%T 13824,15625,17576,21952,24389,35937,42875,50653,54872,59319,68921,
%U 74088,79507,103823,132651,166375,175616,195112,205379,300763,314432
%N Least cube greater than its predecessor such that their difference is a prime or a prime multiplied by a power of two.
%C The sequence was conceived as n^3 is the sum of n primes as shown below:
%C 8=1+7, 27=8+19, 64=27+37, 125=64+61, 343=125+2*109, 729=343+2*193, 1000=729+271 ...
%C Cube roots are 1,2,3,4,5,7,9,10,11,12,14,15,17,18,20,22,24,25,26,...
%t 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_ *)
%Y See A111103 for another version.
%K nonn
%O 1,2
%A _Giovanni Teofilatto_, Oct 14 2005
%E Edited and extended by _Robert G. Wilson v_, Oct 18 2005
%E Name clarified by _Peter Munn_, Jun 17 2021
|
