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

Author

M. F. Hasler, Jul 25 2013

Keywords

• nonn

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

Examples

			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.
		

Crossrefs

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

Programs

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

Extensions

More terms from Michel Marcus, Nov 10 2014