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A255857
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Least k > 0 such that gcd(k^n+7,(k+1)^n+7) > 1, or 0 if there is no such k.
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2
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1, 0, 14, 320, 56, 675113, 224, 13, 5, 283, 33, 192, 26, 242, 5, 2, 10, 140, 5, 50, 142, 29, 18, 605962, 11, 97, 234881024, 951, 5, 3332537854, 14
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OFFSET
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0,3
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COMMENTS
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See A118119, which is the main entry for this class of sequences.
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LINKS
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EXAMPLE
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For n=0, gcd(k^0+7, (k+1)^0+7) = gcd(8, 8) = 8 for any k > 0, therefore a(0)=1 is the smallest possible positive value.
For n=1, gcd(k^n+7, (k+1)^n+7) = gcd(k+7, k+8) = 1, therefore a(1)=0.
For n=2, we have gcd(14^2+7, 15^2+7) = gcd(203, 232) = 29, and the pair (k,k+1)=(14,15) is the smallest which yields a gcd > 1, therefore a(2)=14.
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MATHEMATICA
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A255857[n_] := Module[{m = 1}, While[GCD[m^n + 7, (m + 1)^n + 7] <= 1, m++]; m]; Join[{1, 0}, Table[A255857[n], {n, 2, 25}]] (* Robert Price, Oct 15 2018 *)
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PROG
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(PARI) a(n, c=7, L=10^7, S=1)={n!=1&&for(a=S, L, gcd(a^n+c, (a+1)^n+c)>1&&return(a))}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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