cp's OEIS Frontend

A045911 Neither a cube nor the sum of a nonnegative cube and a prime.

%I A045911 #33 Aug 14 2025 06:06:21
%S A045911 9,16,22,26,28,33,35,36,52,57,63,65,76,78,82,85,92,96,99,112,118,119,
%T A045911 120,122,126,129,133,141,146,155,160,169,170,183,185,188,202,209,210,
%U A045911 217,225,236,244,246,248,267,273,280,286,300,302,309,326
%N A045911 Neither a cube nor the sum of a nonnegative cube and a prime.
%C A045911 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 A045911 From _Daniel Forgues_, Feb 15 2013: (Start)
%C A045911 The graph seems to suggest either that (is there a conjecture?):
%C A045911   * the sequence grows extremely fast (fewer and fewer integers survive),
%C A045911   * the sequence is finite (at some point, no more integers survive).
%C A045911 If the sequence is not finite, what then is the asymptotic behavior?
%C A045911 Growth pattern (why is there an exponential growth interlude?):
%C A045911   * up to about n = 2000 the growth is subexponential (from slightly superlinear, progressing towards exponential growth),
%C A045911   * from about n = 2000 to 5000 the growth is nearly exponential,
%C A045911   * above n = 5000 the growth becomes superexponential (taking off from exponential growth) (there might be a last finite integer term!). (End)
%D A045911 Computed by James Van Buskirk, who finds 6195 solutions between 0 and 3000000000.
%H A045911 D. Wilson, <a href="/A045911/b045911.txt">Table of n, a(n) for n = 1..6195</a>
%o A045911 (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 A045911 Cf. A211167.
%K A045911 nonn
%O A045911 1,1
%A A045911 John Robertson (Jpr2718(AT)aol.com)