A356295 Numbers that are not the sum of a nonnegative cube and a prime.

1, 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, 216, 217, 225, 236, 244, 246, 248, 267, 273, 280, 286, 300, 302, 309, 326, 328, 330, 342

Offset

1,2

Comments

It is conjectured that the subsequence of noncube terms, A045911, is finite (has 6195 terms). But there are infinitely many cubes in this sequence: k^3 if a term if and only if k^3 - (k-1)^3 = 3*k^2 - 3*k + 1 is a nonprime (k-1 is in A257772). For example, for k == 2, 6 (mod 7), 3*k^2 - 3*k + 1 is divisible by 7, so k^3 is a term for k == 2, 6 (mod 7) and k > 2.

Links

Table of n, a(n) for n=1..58.

Example

9 is a term since neither 9 - 0^3 = 9 nor 9 - 1^3 = 8 is a prime.

Prog

(PARI) isA356295(n) = for(m=0, sqrtnint(n, 3), if(isprime(n-m^3), return(0))); return(1)

Crossrefs

Indices of 0 in A302354.

Equals A045911 U {(A257772(n)+1)^3}.

Cf. A014090.

Sequence in context: A072836 A068824 A095961 * A045911 A287186 A134256

Adjacent sequences: A356292 A356293 A356294 * A356296 A356297 A356298

Keyword

nonn

Author

Jianing Song, Aug 03 2022

Status

approved