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A210253 Number of distinct residues of all factorials mod 2^n. 2
1, 2, 3, 4, 5, 6, 8, 8, 9, 10, 11, 13, 14, 16, 16, 16, 17, 18, 19, 20, 22, 24, 24, 25, 26, 27, 29, 30, 32, 32, 32, 32, 33, 34, 35, 36, 37, 40, 40, 41, 42, 43, 45, 46, 48, 48, 48, 49, 50, 51, 52, 54, 56, 56, 57, 58, 59, 61, 62, 64, 64, 64, 64, 64, 65, 66, 67 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Theorem. For n>=1, a(n) = A007843(n) - A210255(n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

Let n=2. We have modulo 4: 0!=1!==1, 2!==3!==2, for n>=4, n!==0. Thus the distinct residues are 0,1,2. Therefore, a(2) = 3.

MAPLE

a:= proc(n) local p, m, i, s;

      p:= 2^n;

      m:= 1;

      s:= {};

      for i to p while m<>0 do m:= m*i mod p; s:=s union {m} od;

      nops(s)

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 20 2012

CROSSREFS

Cf. A000142, A007814.

Sequence in context: A262374 A145518 A256221 * A130916 A003965 A214964

Adjacent sequences:  A210250 A210251 A210252 * A210254 A210255 A210256

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Mar 19 2012

STATUS

approved

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Last modified April 27 10:54 EDT 2017. Contains 285512 sequences.