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A255860
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Least m > 0 such that gcd(m^n+10, (m+1)^n+10) > 1, or 0 if there is no such m.
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2
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1, 0, 20, 3, 2, 3, 320, 874, 6, 33, 1, 124, 465, 23433448460229, 81920, 3, 2, 82, 65, 2101, 1, 3, 3, 2398892314, 7270, 3, 11, 21, 2, 97546469, 1, 765170730, 6, 15, 3, 3, 23, 370460325141871548, 29206018, 3, 1
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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(m^0+10, (m+1)^0+10) = gcd(11, 11) = 11 for any m > 0, therefore a(0)=1 is the smallest possible positive value.
For n=1, gcd(m^n+10, (m+1)^n+10) = gcd(m+10, m+11) = 1, therefore a(1)=0.
For n=2, we have gcd(20^2+10, 21^2+10) = gcd(410, 451) = 41, and the pair (m,m+1)=(20,21) is the smallest which yields a GCD > 1, therefore a(2)=20.
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MATHEMATICA
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A255860[n_] := Module[{m = 1}, While[GCD[m^n + 10, (m + 1)^n + 10] <= 1, m++]; m]; Join[{1, 0}, Table[A255860[n], {n, 2, 12}]] (* Robert Price, Oct 16 2018 *)
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PROG
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(PARI) a(n, c=10, 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,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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