

A255864


Least m > 0 such that gcd(m^n+14, (m+1)^n+14) > 1, or 0 if there is no such m.


2



1, 0, 1, 12, 1, 15, 1, 2, 1, 1929501, 1, 13228907223310811104028677, 1, 94, 1, 11, 1, 85364353, 1, 1563, 1, 49, 1, 9258095644888888790279763522646107297983, 1, 23, 1, 66, 1
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OFFSET

0,4


COMMENTS

See A118119, which is the main entry for this class of sequences.
a(29) with 141 decimal digits is too large to include here (see bfile).


LINKS

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


FORMULA

a(2k) = 1 for k>=0, because gcd(1^(2k)+14, 2^(2k)+14) = gcd(15, 4^k1) >= 3, since 4^k1 = 11 = 0 (mod 3).


EXAMPLE

For n=1, gcd(m^n+14, (m+1)^n+14) = gcd(m+14, m+15) = 1, therefore a(1)=0.
For n=0 and n=2, see formula with k=0 and k=1.
For n=3, gcd(12^3+14, 13^3+14) = 67, and (m, m+1) = (12, 13) is the smallest pair which yields a GCD > 1 here.


MATHEMATICA

A255864[n_] := Module[{m = 1}, While[GCD[m^n + 14, (m + 1)^n + 14] <= 1, m++]; m]; Join[{1, 0}, Table[A255864[n], {n, 2, 10}]] (* Robert Price, Oct 16 2018 *)


PROG

(PARI) a(n, c=14, 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, A255852A255869
Sequence in context: A059857 A322762 A070649 * A056583 A281823 A139724
Adjacent sequences: A255861 A255862 A255863 * A255865 A255866 A255867


KEYWORD

nonn,hard


AUTHOR

M. F. Hasler, Mar 09 2015


EXTENSIONS

a(11)a(40) from Max Alekseyev, Aug 06 2015


STATUS

approved



