A255860 - OEIS

%I #23 Oct 16 2018 17:26:37

%S 1,0,20,3,2,3,320,874,6,33,1,124,465,23433448460229,81920,3,2,82,65,

%T 2101,1,3,3,2398892314,7270,3,11,21,2,97546469,1,765170730,6,15,3,3,

%U 23,370460325141871548,29206018,3,1

%N Least m > 0 such that gcd(m^n+10, (m+1)^n+10) > 1, or 0 if there is no such m.

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

%e 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.

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

%e 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.

%t 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 *)

%o (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))}

%Y Cf. A118119, A255832, A255852-A255869

%K nonn,hard

%O 0,3

%A _M. F. Hasler_, Mar 08 2015

%E a(13)-a(36) from _Hiroaki Yamanouchi_, Mar 13 2015

%E a(37)-a(40) from _Max Alekseyev_, Aug 06 2015