A122385 - OEIS

A122385

Smallest m such that (n^2 mod m) = (m^2 mod n).

1, 2, 2, 2, 4, 5, 5, 3, 3, 8, 9, 6, 10, 11, 4, 4, 14, 6, 16, 10, 8, 18, 19, 5, 5, 22, 9, 12, 11, 8, 26, 6, 6, 29, 6, 6, 14, 33, 26, 20, 36, 16, 37, 22, 12, 40, 41, 7, 7, 10, 45, 26, 47, 18, 21, 15, 38, 22, 52, 27, 54, 55, 8, 8, 58, 59, 60, 34, 39, 12, 19, 12, 65, 66, 15, 29, 69, 70, 71

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OFFSET

1,2

COMMENTS

A122388(n) = n^2 mod a(n) = a(n)^2 mod n;

A122386(n) = a(a(n));

a(A122387(n)) = n, a(m) <> n for m < A122387(n).

LINKS

Table of n, a(n) for n=1..79.

EXAMPLE

10^2 mod 1 = 0 <> 1^2 mod 10 = 1,

10^2 mod 2 = 0 <> 2^2 mod 10 = 4,

10^2 mod 3 = 1 <> 3^2 mod 10 = 9,

10^2 mod 4 = 0 <> 4^2 mod 10 = 6,

10^2 mod 5 = 0 <> 5^2 mod 10 = 5,

10^2 mod 6 = 4 <> 6^2 mod 10 = 6,

10^2 mod 7 = 2 <> 7^2 mod 10 = 9,

10^2 mod 8 = 4 = 8^2 mod 10, therefore a(10) = 8.

MATHEMATICA

s={}; Do[m=0; Until[Mod[n^2, m]==Mod[m^2, n], m++]; AppendTo[s, m] , {n, 79}]; s (* James C. McMahon, Oct 27 2024 *)

CROSSREFS

Sequence in context: A240327 A308771 A007495 * A035002 A032578 A351976

Adjacent sequences: A122382 A122383 A122384 * A122386 A122387 A122388

KEYWORD

nonn,changed

AUTHOR

Reinhard Zumkeller, Sep 01 2006

STATUS

approved