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A255868 Least m > 0 such that gcd(m^n+18, (m+1)^n+18) > 1, or 0 if there is no such m.

%I A255868 #12 Oct 16 2018 17:24:21
%S A255868 1,0,36,5,8,193801631,7,16280817091929,5,4,9216,
%T A255868 815167161742047217904392262,7,46,20,5,19,1837,1,224,8,7,56,13215457,
%U A255868 5,130689,221,4,5,1167507,7,9708,65,7,20,63,1,4248,5,5,5,527010,7
%N A255868 Least m > 0 such that gcd(m^n+18, (m+1)^n+18) > 1, or 0 if there is no such m.
%C A255868 See A118119, which is the main entry for this class of sequences.
%e A255868 For n=0, gcd(m^0+18, (m+1)^0+18) = gcd(19, 19) = 19, therefore a(0)=1, the smallest possible (positive) m-value.
%e A255868 For n=1, gcd(m^n+18, (m+1)^n+18) = gcd(m+18, m+19) = 1, therefore a(1)=0.
%e A255868 For n=2, gcd(36^2+18, 37^2+18) = 73 and (m, m+1) = (36, 37) is the smallest pair which yields a GCD > 1 here.
%t A255868 A255868[n_] :=  Module[{m = 1}, While[GCD[m^n + 18, (m + 1)^n + 18] <= 1, m++]; m]; Join[{1, 0}, Table[A255868[n], {n, 2, 10}]] (* _Robert Price_, Oct 16 2018 *)
%o A255868 (PARI) a(n,c=18,L=10^7,S=1)={n!=1 && for(a=S,L,gcd(a^n+c,(a+1)^n+c)>1 && return(a))}
%Y A255868 Cf. A118119, A255832, A255852-A255869
%K A255868 nonn,hard
%O A255868 0,3
%A A255868 _M. F. Hasler_, Mar 09 2015
%E A255868 a(5)-a(42) from _Max Alekseyev_, Aug 06 2015