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Neither a cube nor the sum of a nonnegative cube and a prime.
7

%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)