A097794 Least k such that the absolute value of k^n-n is prime or zero if no such k exists.

3, 2, 1, 1, 4, 1, 60, 1, 2, 21, 28, 1, 2, 1, 28, 0, 234, 1, 2, 1, 2, 159, 10, 1, 68, 145, 0, 69, 186, 1, 32, 1, 26, 261, 4, 0, 8, 1, 62, 3, 22, 1, 6, 1, 8, 945, 76, 1, 116, 129, 382, 93, 330, 1, 2, 555, 224, 1359, 78, 1, 62, 1, 110, 0, 1032, 37, 462, 1, 100, 9, 88, 1, 1416, 1, 218

Offset: 1

Author

T. D. Noe, Aug 24 2004

Keywords

• nonn

Comments

Because the polynomial x^n - n is reducible for n in A097764, a(n) is 0 for n=16, 27, 36, 64, 100,.... Although x^4-4 is reducible, the factor x^2-2 is -1 for x=1.

Crossrefs

Cf. A097764 (n such that x^n-n is reducible), A072883 (least k such that k^n+n is prime).

Programs

Mathematica

Table[If[MemberQ[{16, 27, 36, 64, 100}, n], 0, k=1; While[ !PrimeQ[k^n-n], k++ ]; k], {n, 100}]