%I #28 May 19 2013 10:21:47
%S 9,16,22,26,28,33,35,36,52,57,63,65,76,78,82,85,92,96,99,112,118,119,
%T 120,122,126,129,133,141,146,155,160,169,170,183,185,188,202,209,210,
%U 217,225,236,244,246,248,267,273,280,286,300,302,309,326
%N Neither a cube nor the sum of a nonnegative cube and a prime.
%C Numbers of the form 1 + k^3, as {9, 28, 65, 126, 217, 344, 513, 730, 1001, 1332, 1729, ...}, are allowed unless they can also be expressed as p + j^3 for some prime p (thus excluding {344, 513, 1001, 1729, ...}). - _Daniel Forgues_, Feb 13 2013
%C Contribution from _Daniel Forgues_, Feb 15 2013. (Start)
%C The graph seems to suggest either that (is there a conjecture?):
%C * the sequence grows extremely fast (fewer and fewer integers survive),
%C * the sequence is finite (at some point, no more integers survive).
%C If the sequence is not finite, what then is the asymptotic behavior?
%C Growth pattern (why is there an exponential growth interlude?):
%C * up to about n = 2000 the growth is subexponential (from slightly superlinear, progressing towards exponential growth),
%C * from about n = 2000 to 5000 the growth is nearly exponential,
%C * above n = 5000 the growth becomes superexponential (taking off from exponential growth) (there might be a last finite integer term!). (end)
%D Computed by James Van Buskirk, who finds 6195 solutions between 0 and 3000000000.
%H D. Wilson, <a href="/A045911/b045911.txt">Table of n, a(n) for n = 1..6195</a>
%o (PARI) isA045911(n) = {if (ispower(n, 3), return (0)); forprime(p=2, n, if (ispower(n-p, 3), return (0));); return (1);} \\ _Michel Marcus_, May 19 2013
%Y Cf. A211167.
%K nonn
%O 1,1
%A John Robertson (Jpr2718(AT)aol.com)