A378765 (Exponent of the highest power of 2 that divides n!), reduced modulo 10.

0, 0, 1, 1, 3, 3, 4, 4, 7, 7, 8, 8, 0, 0, 1, 1, 5, 5, 6, 6, 8, 8, 9, 9, 2, 2, 3, 3, 5, 5, 6, 6, 1, 1, 2, 2, 4, 4, 5, 5, 8, 8, 9, 9, 1, 1, 2, 2, 6, 6, 7, 7, 9, 9, 0, 0, 3, 3, 4, 4, 6, 6, 7, 7, 3, 3, 4, 4, 6, 6, 7, 7, 0, 0, 1, 1, 3, 3, 4, 4, 8, 8, 9, 9, 1, 1, 2, 2, 5, 5, 6, 6, 8, 8, 9, 9, 4, 4, 5, 5, 7, 7, 8, 8, 1

Offset

0,5

Comments

Is not periodic, but the distributions of the ten results is normal.

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..10000

Formula

a(n) = A011371(n) mod 10.

Example

a(100) = 7 because 2^50, 4^25, 8^12, 16^6, 32^3, 64^1 all divide 100, and the sum of their exponents is 97. 97 (mod 10) = 7.

Mathematica

a[n_] := Mod[ Plus @@ Rest@ NestWhileList[ Floor[#/2] &, n, UnsameQ[##] &, All], 10]; Array[a, 105, 0] (* or *)
a[n_] := Mod[n - DigitCount[n, 2, 1], 10]; Array[a, 105, 0]
Table[Mod[IntegerExponent[n!, 2], 10], {n, 0, 110}] (* Harvey P. Dale, Feb 22 2026 *)

Prog

(PARI) a(n) = (n - hammingweight(n)) % 10; \\ Michel Marcus, Dec 29 2024

Crossrefs

Cf. A011371, A095190, A218451.

Sequence in context: A007768 A389672 A180018 * A011371 A325123 A097355

Adjacent sequences: A378762 A378763 A378764 * A378766 A378767 A378768

Keyword

easy,nonn

Author

Robert G. Wilson v, Dec 28 2024

Status

approved