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A255861 Least m > 0 such that gcd(m^n+11, (m+1)^n+11) > 1, or 0 if there is no such m. 2
1, 0, 1, 2, 1, 23, 1, 19010820161, 1, 7, 1, 360, 1, 41953103, 1, 4, 1, 638386957517954762853, 1, 38884, 1, 2, 1, 2852, 1, 23, 1, 102, 1, 8384, 1, 36556, 1, 33, 1, 37, 1, 336, 1, 2, 1, 1123, 1, 19734, 1, 9, 1, 135356, 1, 399351, 1, 33, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

LINKS

Table of n, a(n) for n=0..52.

FORMULA

a(2k)=1 for k>=0, because gcd(1^(2k)+11, 2^(2k)+11) = gcd(12, 4^k-1) = 3.

EXAMPLE

For n=1, gcd(m^n+11, (m+1)^n+11) = gcd(m+11, m+12) = 1, therefore a(1)=0.

For n=2, we have gcd(2^2+11, 3^2+11) = gcd(15, 20) = 5, and the pair (m,m+1)=(2,3) is the smallest which yields a GCD > 1, therefore a(2)=2.

MATHEMATICA

A255861[n_] := Module[{m = 1}, While[GCD[m^n + 11, (m + 1)^n + 11] <= 1, m++]; m]; Join[{1, 0}, Table[A255861[n], {n, 2, 6}]] (* Robert Price, Oct 16 2018 *)

PROG

(PARI) a(n, c=11, 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: A330354 A200859 A127607 * A059360 A279308 A108778

Adjacent sequences:  A255858 A255859 A255860 * A255862 A255863 A255864

KEYWORD

nonn

AUTHOR

M. F. Hasler, Mar 08 2015

EXTENSIONS

a(7)-a(48) from Hiroaki Yamanouchi, Mar 12 2015

a(49)-a(52) from Max Alekseyev, Aug 06 2015

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)