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 A255869 Least m > 0 such that gcd(m^n+19, (m+1)^n+19) > 1, or 0 if there is no such m. 20
 1, 0, 3, 2408, 1, 3976, 608, 28, 1, 88, 23, 464658, 1, 319924724, 3, 7, 1, 1628, 138, 2219409, 1, 6, 5, 594, 1, 872, 3, 92, 1, 392, 65, 2278155, 1, 3755866, 4793, 13, 1, 7873, 3, 614294, 1, 448812437, 5 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See A118119, which is the main entry for this class of sequences. a(43) <= 8153777984244162781089834. - Max Alekseyev, Aug 06 2015 LINKS FORMULA a(4k) = 1 for k>=0, because gcd(1^(4k)+19, 2^(4k)+19) = gcd(20, 16^k-1) >= 5 since 16 = 1 (mod 5). EXAMPLE For n=0 and n=4, see formula with k=0 resp. k=1. For n=1, gcd(m^n+19, (m+1)^n+19) = gcd(m+19, m+20) = 1, therefore a(1)=0. For n=2, gcd(3^2+19, 4^2+19) = 7 and (m,m+1) = (3,4) is the smallest pair which yields a GCD > 1 here. MATHEMATICA A255869[n_] := Module[{m = 1}, While[GCD[m^n + 19, (m + 1)^n + 19] <= 1, m++]; m]; Join[{1, 0}, Table[A255869[n], {n, 2, 12}]] (* Robert Price, Oct 16 2018 *) PROG (PARI) a(n, c=19, 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-A255868 Sequence in context: A293099 A286715 A081176 * A289650 A171361 A203687 Adjacent sequences:  A255866 A255867 A255868 * A255870 A255871 A255872 KEYWORD nonn,hard AUTHOR M. F. Hasler, Mar 09 2015 EXTENSIONS a(13)-a(40) from Hiroaki Yamanouchi, Mar 12 2015 a(41)-a(42) from Max Alekseyev, Aug 06 2015 STATUS approved

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Last modified August 8 06:27 EDT 2020. Contains 336290 sequences. (Running on oeis4.)