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A255855
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Least k > 0 such that gcd(k^n+5, (k+1)^n+5) > 1, or 0 if there is no such k.
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2
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1, 0, 1, 5, 1, 533360, 1, 55, 1, 7, 1, 796479131355665831357, 1, 41, 1, 5, 1, 3775, 1, 42296, 1, 7, 1, 653246700175064613889, 1, 21, 1, 5, 1, 1619, 1, 42842, 1, 7, 1, 2945, 1, 323371, 1, 5, 1, 1102221, 1, 633524110177, 1, 7, 1
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OFFSET
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0,4
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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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FORMULA
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a(2k)=1 for k>=0, because gcd(1^(2k)+5,2^(2k)+5) = gcd(6,4^k-1) = 3.
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EXAMPLE
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For n=1, gcd(k^n+5, (k+1)^n+5) = gcd(k+5, k+6) = 1, therefore a(1)=0.
For n=2k, see formula.
For n=3, we have gcd(5^3+5, 6^3+5) = 13, and the pair (k,k+1)=(5,6) is the smallest which yields a GCD > 1, therefore a(3)=5.
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MATHEMATICA
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A255855[n_] := Module[{m = 1}, While[GCD[m^n + 5, (m + 1)^n + 5] <= 1, m++]; m]; Join[{1, 0}, Table[A255855[n], {n, 2, 10}]]
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PROG
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(PARI) a(n, c=5, L=10^7, S=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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