A255857 Least k > 0 such that gcd(k^n+7,(k+1)^n+7) > 1, or 0 if there is no such k.

1, 0, 14, 320, 56, 675113, 224, 13, 5, 283, 33, 192, 26, 242, 5, 2, 10, 140, 5, 50, 142, 29, 18, 605962, 11, 97, 234881024, 951, 5, 3332537854, 14

Offset

0,3

Comments

See A118119, which is the main entry for this class of sequences.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 0..36

Example

For n=0, gcd(k^0+7, (k+1)^0+7) = gcd(8, 8) = 8 for any k > 0, therefore a(0)=1 is the smallest possible positive value.
For n=1, gcd(k^n+7, (k+1)^n+7) = gcd(k+7, k+8) = 1, therefore a(1)=0.
For n=2, we have gcd(14^2+7, 15^2+7) = gcd(203, 232) = 29, and the pair (k,k+1)=(14,15) is the smallest which yields a gcd > 1, therefore a(2)=14.

Mathematica

A255857[n_] := Module[{m = 1}, While[GCD[m^n + 7, (m + 1)^n + 7] <= 1, m++]; m]; Join[{1, 0}, Table[A255857[n], {n, 2, 25}]] (* Robert Price, Oct 15 2018 *)

Prog

(PARI) a(n, c=7, L=10^7, S=1)={n!=1&&for(a=S, L, gcd(a^n+c, (a+1)^n+c)>1&&return(a))}

Crossrefs

Cf. A118119, A255832, A255852-A255869

Sequence in context: A213466 A303488 A341501 * A239782 A294040 A035018

Adjacent sequences: A255854 A255855 A255856 * A255858 A255859 A255860

Keyword

nonn

Author

M. F. Hasler, Mar 08 2015

Extensions

a(26)-a(36) from Hiroaki Yamanouchi, Mar 12 2015

Status

approved