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A255859
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Least m > 0 such that gcd(m^n+9,(m+1)^n+9) > 1, or 0 if there is no such m.
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4
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1, 0, 18, 533, 1, 32, 288, 484, 1, 364, 6, 176427, 1, 31239, 533, 8, 1, 8424432925592889329288197322308900672459420460792433, 30, 16561, 1, 4, 6, 349, 1, 32, 546, 2579, 1, 375766, 11, 5061867704425915, 1, 5620, 6, 8, 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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FORMULA
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a(4k)=1 for k>=0, because gcd(1^(4k)+9, 2^(4k)+9) = gcd(10, 16^k-1) = 5.
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EXAMPLE
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For n=1, gcd(m^n+9, (m+1)^n+9) = gcd(m+9, m+10) = 1, therefore a(1)=0.
For n=2, we have gcd(18^2+9, 19^2+9) = gcd(333, 370) = 37, and the pair (m,m+1)=(18,19) is the smallest which yields a GCD > 1, therefore a(2)=37.
For n=4k, see formula.
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MATHEMATICA
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A255859[n_] := Module[{m = 1}, While[GCD[m^n + 9, (m + 1)^n + 9] <= 1, m++]; m]; Join[{1, 0}, Table[A255859[n], {n, 2, 16}]] (* Robert Price, Oct 16 2018 *)
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PROG
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(PARI) a(n, c=9, 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,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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