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A255860 Least m > 0 such that gcd(m^n+10, (m+1)^n+10) > 1, or 0 if there is no such m. 2
1, 0, 20, 3, 2, 3, 320, 874, 6, 33, 1, 124, 465, 23433448460229, 81920, 3, 2, 82, 65, 2101, 1, 3, 3, 2398892314, 7270, 3, 11, 21, 2, 97546469, 1, 765170730, 6, 15, 3, 3, 23, 370460325141871548, 29206018, 3, 1 (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

Table of n, a(n) for n=0..40.

EXAMPLE

For n=0, gcd(m^0+10, (m+1)^0+10) = gcd(11, 11) = 11 for any m > 0, therefore a(0)=1 is the smallest possible positive value.

For n=1, gcd(m^n+10, (m+1)^n+10) = gcd(m+10, m+11) = 1, therefore a(1)=0.

For n=2, we have gcd(20^2+10, 21^2+10) = gcd(410, 451) = 41, and the pair (m,m+1)=(20,21) is the smallest which yields a GCD > 1, therefore a(2)=20.

MATHEMATICA

A255860[n_] := Module[{m = 1}, While[GCD[m^n + 10, (m + 1)^n + 10] <= 1, m++]; m]; Join[{1, 0}, Table[A255860[n], {n, 2, 12}]] (* Robert Price, Oct 16 2018 *)

PROG

(PARI) a(n, c=10, 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: A040399 A040390 A040391 * A195600 A118295 A070645

Adjacent sequences:  A255857 A255858 A255859 * A255861 A255862 A255863

KEYWORD

nonn,hard

AUTHOR

M. F. Hasler, Mar 08 2015

EXTENSIONS

a(13)-a(36) from Hiroaki Yamanouchi, Mar 13 2015

a(37)-a(40) from Max Alekseyev, Aug 06 2015

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)