A290542 - OEIS

%I #25 Sep 08 2022 08:46:19

%S 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,

%T 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,

%U 0,2,0,0,0,0,0,2,0,0,0,2,0,4,0,0,0,2,0

%N 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.

%H Antti Karttunen, <a href="/A290542/b290542.txt">Table of n, a(n) for n = 4..20000</a>

%F a(A000040(n)) = 2 for n >= 3.

%F a(A001567(n)) = 2 for n >= 1.

%F a(A006935(n)) = 2 for n >= 2.

%F For n >= 3, a(x) = 2*A010051(x), where x = A000040(n).

%t Table[SelectFirst[Range[2, Sqrt@ n], PowerMod[#, n , n] == Mod[#, n] &] /. k_ /; MissingQ@ k -> 0, {n, 4, 90}] (* _Michael De Vlieger_, Aug 09 2017 *)

%o (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;

%o (PARI) a(n) = for (k=2, sqrtint(n), if (Mod(k, n)^n == k, return(k));); return (0); \\ _Michel Marcus_, Aug 19 2017

%Y Cf. A010051, A290543.

%K nonn

%O 4,2

%A _Arkadiusz Wesolowski_, Aug 05 2017