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A290542
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a(n) is the least integer k in the interval [2, sqrt(n)] such that k^n == k (mod n), or 0 if no such integer exists.
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2
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0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 4, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 5, 3, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 4, 0, 0, 0, 2, 0
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OFFSET
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4,2
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LINKS
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FORMULA
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MATHEMATICA
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Table[SelectFirst[Range[2, Sqrt@ n], PowerMod[#, n , n] == Mod[#, n] &] /. k_ /; MissingQ@ k -> 0, {n, 4, 90}] (* Michael De Vlieger, Aug 09 2017 *)
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PROG
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(Magma) lst:=[]; for n in [4..90] do r:=Floor(Sqrt(n)); for k in [2..r] do if Modexp(k, n, n) eq k then Append(~lst, k); break; end if; if k eq r then Append(~lst, 0); end if; end for; end for; lst;
(PARI) a(n) = for (k=2, sqrtint(n), if (Mod(k, n)^n == k, return(k)); ); return (0); \\ Michel Marcus, Aug 19 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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