A065293 Number of values of s, 0 <= s <= n-1, such that 2^s mod n = s.

1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 1, 0, 0, 3, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1

Offset

1,21

Links

Michel Marcus, Table of n, a(n) for n = 1..1000

Example

For n=5 we have (2^0) mod 5 = 1, (2^1) mod 5 = 2, (2^2) mod 5 = 4, (2^3) mod 5 = 3, (2^4) mod 5 = 1. Only for s=3 does (2^s) mod 5=s, so a(5)=1

Mathematica

Table[Count[Range[0, n - 1], _?(Mod[2^#, n] == # &)], {n, 105}] (* Michael De Vlieger, Jun 19 2018 *)
Table[Count[Range[0, n-1], _?(PowerMod[2, #, n]==#&)], {n, 110}] (* Harvey P. Dale, Aug 02 2024 *)

Prog

(PARI) a(n) = sum(s=0, n-1, Mod(2, n)^s == s); \\ Michel Marcus, Jun 19 2018

Crossrefs

Cf. A065294.

Sequence in context: A145708 A138532 A339445 * A364377 A164615 A182034

Adjacent sequences: A065290 A065291 A065292 * A065294 A065295 A065296

Keyword

nonn

Author

Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 28 2001

Extensions

a(1) corrected by Michel Marcus, Jun 20 2018

Status

approved