A072883 Least k >= 1 such that k^n + n is prime, or 0 if no such k exists.

1, 1, 2, 1, 2, 1, 16, 3, 2, 1, 32, 1, 118, 417, 2, 1, 14, 1, 22, 81, 76, 1, 12, 55, 28, 15, 0, 1, 110, 1, 232, 117, 230, 3, 12, 1, 4, 375, 2, 1, 48, 1, 46, 15, 218, 1, 78, 7, 100, 993, 28, 1, 624, 13, 252, 183, 226, 1, 104, 1, 1348, 777, 1294, 0, 1806, 1, 306, 1815, 10, 1, 30, 1

Offset: 1

Author

Benoit Cloitre, Aug 13 2002

Keywords

• nonn

Comments

Because the polynomial x^n + n is reducible for n in A097792, a(27) and a(64) are 0. Although x^4 + 4 is reducible, the factor x^2 - 2x + 2 is 1 for x=1. - T. D. Noe, Aug 24 2004

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..756

Crossrefs

Cf. A097792 (n such that x^n + n is reducible).

Cf. A239666, A303121, A303122.

Programs

Mathematica

Table[If[MemberQ[{27, 64}, n], 0, k=1; While[ !PrimeQ[k^n+n], k++ ]; k], {n, 100}]
(* Second program: *)
okQ[n_] := n == 4 || IrreduciblePolynomialQ[x^n + n];
a[n_] := If[!okQ[n], 0, s = 1; While[!PrimeQ[s^n + n], s++]; s];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 15 2019, from PARI *)

PARI

isok(n) = (n==4) || polisirreducible(x^n+n);
a(n) = if (!isok(n), 0, my(s=1); while(!isprime(s^n+n), s++); s); \\ adapted by Michel Marcus, Jan 15 2019

PARI

apply( {A072883(n)=if(is_A097792(n), n==4, for(k=1, oo, ispseudoprime(k^n+n) && return(k)))}, [1..99]) \\ M. F. Hasler, Jul 07 2024

Python

from sympy import isprime
def A072883(n):
    if is_A097792(n): return int(n==4)
    for k in range(1,99**9):
        if isprime(k**n+n): return k # M. F. Hasler, Jul 07 2024

Extensions

More terms from T. D. Noe, Aug 24 2004