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

9, 16, 22, 26, 28, 33, 35, 36, 52, 57, 63, 65, 76, 78, 82, 85, 92, 96, 99, 112, 118, 119, 120, 122, 126, 129, 133, 141, 146, 155, 160, 169, 170, 183, 185, 188, 202, 209, 210, 217, 225, 236, 244, 246, 248, 267, 273, 280, 286, 300, 302, 309, 326

Offset: 1

Author

John Robertson (Jpr2718(AT)aol.com)

Keywords

• nonn

Comments

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

From Daniel Forgues, Feb 15 2013: (Start)

The graph seems to suggest either that (is there a conjecture?):

* the sequence grows extremely fast (fewer and fewer integers survive),

* the sequence is finite (at some point, no more integers survive).

If the sequence is not finite, what then is the asymptotic behavior?

Growth pattern (why is there an exponential growth interlude?):

* up to about n = 2000 the growth is subexponential (from slightly superlinear, progressing towards exponential growth),

* from about n = 2000 to 5000 the growth is nearly exponential,

* above n = 5000 the growth becomes superexponential (taking off from exponential growth) (there might be a last finite integer term!). (End)

References

• Computed by James Van Buskirk, who finds 6195 solutions between 0 and 3000000000.

Links

• D. Wilson, Table of n, a(n) for n = 1..6195

Crossrefs

Cf. A211167.

Programs

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