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A255857 Least k > 0 such that gcd(k^n+7,(k+1)^n+7) > 1, or 0 if there is no such k. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 12 19:54 EDT 2022. Contains 356077 sequences. (Running on oeis4.)