A072943 Least nonnegative integer k such that n + k^3 is prime, or -1 if no such k exists.

1, 0, 0, 1, 0, 1, 0, -1, 2, 1, 0, 1, 0, 3, 2, 1, 0, 1, 0, 3, 2, 1, 0, 5, 4, 3, -1, 1, 0, 1, 0, 3, 2, 3, 2, 1, 0, 5, 2, 1, 0, 1, 0, 3, 2, 1, 0, 5, 4, 11, 2, 1, 0, 5, 6, 3, 8, 1, 0, 1, 0, 3, 2, -1, 2, 1, 0, 5, 10, 1, 0, 1, 0, 3, 2, 3, 6, 1, 0, 3, 2, 1, 0, 13, 4, 3, 4, 1, 0, 7, 6, 9, 2, 9, 2, 1, 0, 5, 2, 1

Offset

1,9

Comments

For n = 2^3, 3^3, 4^3,...., a(n) = -1 since, say, 2^3 + k^3 cannot be prime for nonnegative k (it can be factored by the sum of cubes formula).

a(n) = 0 if and only if n is prime. - Iain Fox, Dec 29 2017

Links

Iain Fox, Table of n, a(n) for n = 1..10000

Example

a(9) = 2 since k = 2 is the least nonnegative integer such that 9 + k^3 is prime.

Mathematica

Array[Which[PrimeQ@ #, 0, And[# > 1, IntegerQ@ Power[#, 1/3]], -1, True, Block[{k = 1}, While[! PrimeQ[# + k^3], k++]; k]] &, 100] (* Michael De Vlieger, Dec 30 2017 *)

Prog

(PARI) a(n) = if(round(n^(1/3))^3 == n && n!=1, return(-1)); for(k=0, +oo, if(isprime(n + k^3), return(k))) \\ Iain Fox, Dec 29 2017

Crossrefs

Sequence in context: A229297 A116675 A123022 * A372596 A072175 A280712

Adjacent sequences: A072940 A072941 A072942 * A072944 A072945 A072946

Keyword

sign

Author

Joseph L. Pe, Aug 14 2002

Status

approved