A356295 - OEIS

%I #6 Aug 03 2022 11:04:32

%S 1,9,16,22,26,28,33,35,36,52,57,63,65,76,78,82,85,92,96,99,112,118,

%T 119,120,122,126,129,133,141,146,155,160,169,170,183,185,188,202,209,

%U 210,216,217,225,236,244,246,248,267,273,280,286,300,302,309,326,328,330,342

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

%C 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.

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

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

%Y Indices of 0 in A302354.

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

%Y Cf. A014090.

%K nonn

%O 1,2

%A _Jianing Song_, Aug 03 2022