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 A186710 a(n) = gcd(k^n + 1, (k+1)^n + 1) for the smallest k at which the GCD exceeds 1. 3
 5, 7, 17, 11, 5, 29, 17, 19, 25, 23, 17, 53, 145, 61, 353, 137, 5, 191, 41, 43, 5, 47, 97, 11, 265, 19, 337, 59, 25, 5953, 257, 67, 5, 29, 17, 223, 5, 157, 17, 83, 145, 173, 89, 19, 5, 283, 353, 29, 12625, 307, 17, 107, 5, 121, 1921, 229, 5, 709, 241, 367, 5, 817, 769, 521, 5, 269, 137, 139, 725, 853, 55969, 293, 745, 61, 17, 29, 265 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS For k=0, the GCD equals 1. Increasing k, the GCD first exceeds 1 at k = A118119(n), and that GCD is a(n). LINKS EXAMPLE a(2) = 5 because 2^2 + 1 = 5 and 3^2+1 = 2*5; a(3) = 7 because 5^3 + 1 = 2*3^2*7 and 6^3 + 1 = 7*31. MAPLE A186710 := proc(n) local k , g; for k from 1 do g := igcd(k^n+1, (k+1)^n+1) ; if g>1 then return g ; end if; end do: end proc: # R. J. Mathar, Mar 07 2011 CROSSREFS Cf. A118119. Sequence in context: A279175 A279875 A185872 * A276717 A318491 A060640 Adjacent sequences:  A186707 A186708 A186709 * A186711 A186712 A186713 KEYWORD nonn AUTHOR Michel Lagneau, Feb 26 2011 STATUS approved

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Last modified May 8 15:54 EDT 2021. Contains 343666 sequences. (Running on oeis4.)