A225765 Least k>0 such that k^3+n is prime, or 0 if there is no such k.

1, 1, 2, 1, 2, 1, 4, 0, 2, 1, 2, 1, 6, 3, 2, 1, 6, 1, 4, 3, 2, 1, 2, 5, 4, 3, 0, 1, 2, 1, 10, 3, 2, 3, 2, 1, 4, 5, 2, 1, 6, 1, 4, 3, 2, 1, 6, 5, 4, 11, 2, 1, 2, 5, 6, 3, 8, 1, 2, 1, 6, 3, 2, 0, 2, 1, 4, 5, 10, 1, 2, 1, 4, 3, 2, 3, 6, 1, 24, 3, 2, 1, 12, 13, 4

Offset

1,3

Comments

See A225768 for motivation.

a(n) = 0 for n = m^3 (m > 1) but are there other cases of a(n)=0? - Zak Seidov, Nov 10 2014

Links

Table of n, a(n) for n=1..85.

Example

a(7)=4 because 1^3+7=8, 2^3+7=15, 3^3+7=34 are all composite, but 4^3+7=71 is prime.
a(8)=0 because x^3+8 = (x+2)(x^2-2x+4) is composite for all integer values x>0.

Prog

(PARI) A225765(a, b=3)={#factor(x^b+a)~==1&for(n=1, 9e9, ispseudoprime(n^b+a)&return(n)); a==1&return(1); print1("/*"factor(x^b+a)"*/")}  \\  For illustrative purpose only: the polynomial is factored to avoid an infinite search loop when it is composite. But this does not exclude that all but one factors might equal 1, therefore the factorization is printed for control before 0 is returned.
(PARI) a(n) = {if ((n!=1) && ispower(n, 3), return (0)); k = 1; while (! isprime(k^3+n), k++); k; } \\ Michel Marcus, Nov 10 2014

Crossrefs

See A085099, A225766, A225767, A225768 for the k^2, k^4, k^5, k^6 analog.

Sequence in context: A331917 A328318 A081169 * A300588 A345257 A030359

Adjacent sequences: A225762 A225763 A225764 * A225766 A225767 A225768

Keyword

nonn

Author

M. F. Hasler, Jul 25 2013

Extensions

More terms from Michel Marcus, Nov 10 2014

Status

approved