A186710 a(n) = gcd(k^n + 1, (k+1)^n + 1) for the smallest k at which the GCD exceeds 1.

5, 7, 17, 11, 5, 29, 17, 19, 25, 23, 17, 53, 145, 61, 353, 137, 5, 191, 41, 43, 5, 47, 97, 11, 265, 19, 337, 59, 25, 5953, 257, 67, 5, 29, 17, 223, 5, 157, 17, 83, 145, 173, 89, 19, 5, 283, 353, 29, 12625, 307, 17, 107, 5, 121, 1921, 229, 5, 709, 241, 367, 5, 817, 769, 521, 5, 269, 137, 139, 725, 853, 55969, 293, 745, 61, 17, 29, 265

Offset

2,1

Comments

For k=0, the GCD equals 1. Increasing k, the GCD first exceeds 1 at k = A118119(n), and that GCD is a(n).

Links

Table of n, a(n) for n=2..78.

Example

a(2) = 5 because 2^2 + 1 = 5 and 3^2+1 = 2*5;
a(3) = 7 because 5^3 + 1 = 2*3^2*7 and 6^3 + 1 = 7*31.

Maple

A186710 := proc(n) local k , g; for k from 1 do g := igcd(k^n+1, (k+1)^n+1) ; if g>1 then return g ; end if; end do: end proc: # R. J. Mathar, Mar 07 2011

Crossrefs

Cf. A118119.

Sequence in context: A279175 A279875 A185872 * A276717 A374777 A318491

Adjacent sequences: A186707 A186708 A186709 * A186711 A186712 A186713

Keyword

nonn

Author

Michel Lagneau, Feb 26 2011

Status

approved