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A255832
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Least m > 0 such that gcd(m^(2n+1)+2, (m+1)^(2n+1)+2) > 1.
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19
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51, 40333, 434, 16, 1234, 78607, 8310, 817172, 473, 116, 22650, 736546059, 22, 1080982, 252, 7809, 644, 1786225573
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OFFSET
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1,1
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COMMENTS
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For n=0 one has gcd(m+2, m+3) = 1 for any m.
See A255852 for the sequence including also even exponents, for which the GCD is > 1 already for m=1 (because gcd(1^2k+2, 2^2k+2) = gcd(3, 2^2k-1) = gcd(3, 4^k-1) = 3), and also for m=4 (because gcd(4^2k+2, 5^2k+2) = gcd(4^2k+2, (5^k-4^k)(5^k+4^k)) >= 3), etc.
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LINKS
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FORMULA
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MATHEMATICA
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A255832[n_] := Module[{m = 1}, While[GCD[m^(2 n + 1) + 2, (m + 1)^(2 n + 1) + 2] <= 1, m++]; m]; Table[A255832[n], {n, 1, 10}] (* Robert Price, Oct 15 2018 *)
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PROG
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(PARI) a(n, c=2, L=10^6)={n=n*2+1; for(a=1, L, gcd(a^n+c, (a+1)^n+c)>1&&return(n))}
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CROSSREFS
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Cf. A118119, A255853, A255853, ... for other variants, corresponding to different constant offsets (+1, +3, ...) in the arguments of gcd.
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KEYWORD
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nonn,more,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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