A186713 For the starting base k = A118119(n), a(n) is the largest value q such that gcd(k^n+1, (k+1)^n+1, ..., (k+q)^n+1) > 1.

1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2

Offset: 2

Author

Michel Lagneau, Feb 26 2011

Keywords

• nonn

Examples

			a(2) = 1 because 2^2+1 = 5 and 3^2+1 = 2*5 => gcd(..) = 5 and q = 1;
a(53) = 3 because
5^53 + 1 = 2 * 3 * 107 * 28838378869 * 599659003321309822423087;
6^53 + 1 = 7 * 107 * 97351567 * 33685364386033 * 71080464397105403;
7^53 + 1 = 2^3 * 107 * 345449549 * 35416476134069*58902316970027001503;
8^53 + 1 = 3^2 * 107 * 6043 * 28059810762433 * 4475130366518102084427698737 => gcd(..) = 107 and q=3.
		

Crossrefs

Cf. A186710, A118119.

Programs

Maple

A186713 := proc(n) local k ,g,q; k := A118119(n) ; for q from 1 do g := igcd(seq((k+i)^n+1,i=0..q)) ; if g=1 then return q-1 ; end if; end do: end proc: # R. J. Mathar, Mar 07 2011

Extensions

a(55), a(56) corrected by R. J. Mathar, Mar 07 2011