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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. 3
1, 0, 36, 5, 8, 193801631, 7, 16280817091929, 5, 4, 9216, 815167161742047217904392262, 7, 46, 20, 5, 19, 1837, 1, 224, 8, 7, 56, 13215457, 5, 130689, 221, 4, 5, 1167507, 7, 9708, 65, 7, 20, 63, 1, 4248, 5, 5, 5, 527010, 7 (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..42.

EXAMPLE

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.

For n=1, gcd(m^n+18, (m+1)^n+18) = gcd(m+18, m+19) = 1, therefore a(1)=0.

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.

MATHEMATICA

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 *)

PROG

(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))}

CROSSREFS

Cf. A118119, A255832, A255852-A255869

Sequence in context: A227168 A100252 A020340 * A289138 A181759 A280679

Adjacent sequences:  A255865 A255866 A255867 * A255869 A255870 A255871

KEYWORD

nonn,hard

AUTHOR

M. F. Hasler, Mar 09 2015

EXTENSIONS

a(5)-a(42) from Max Alekseyev, Aug 06 2015

STATUS

approved

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Last modified September 23 03:34 EDT 2020. Contains 337291 sequences. (Running on oeis4.)