cp's OEIS Frontend

A255861 Least m > 0 such that gcd(m^n+11, (m+1)^n+11) > 1, or 0 if there is no such m.

%I A255861 #24 Oct 16 2018 17:26:50
%S A255861 1,0,1,2,1,23,1,19010820161,1,7,1,360,1,41953103,1,4,1,
%T A255861 638386957517954762853,1,38884,1,2,1,2852,1,23,1,102,1,8384,1,36556,1,
%U A255861 33,1,37,1,336,1,2,1,1123,1,19734,1,9,1,135356,1,399351,1,33,1
%N A255861 Least m > 0 such that gcd(m^n+11, (m+1)^n+11) > 1, or 0 if there is no such m.
%C A255861 See A118119, which is the main entry for this class of sequences.
%F A255861 a(2k)=1 for k>=0, because gcd(1^(2k)+11, 2^(2k)+11) = gcd(12, 4^k-1) = 3.
%e A255861 For n=1, gcd(m^n+11, (m+1)^n+11) = gcd(m+11, m+12) = 1, therefore a(1)=0.
%e A255861 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.
%t A255861 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 *)
%o A255861 (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))}
%Y A255861 Cf. A118119, A255832, A255852-A255869
%K A255861 nonn
%O A255861 0,4
%A A255861 _M. F. Hasler_, Mar 08 2015
%E A255861 a(7)-a(48) from _Hiroaki Yamanouchi_, Mar 12 2015
%E A255861 a(49)-a(52) from _Max Alekseyev_, Aug 06 2015