A276350 Sum of digits of 1/n in factorial base.

1, 1, 2, 3, 5, 1, 11, 3, 7, 4, 25, 2, 42, 10, 4, 6, 65, 6, 94, 2, 7, 24, 125, 1, 26, 46, 18, 10, 182, 4, 265, 14, 33, 65, 9, 5, 394, 84, 33, 3, 449, 8, 471, 25, 6, 121, 570, 5, 48, 21, 62, 40, 619, 13, 18, 8, 85, 150, 847, 2, 1020, 263, 9, 13, 38, 31, 1064, 60

Offset

1,3

Comments

See the Wikipedia link for the construction method of 1/n in factorial base.

For n>1, A002034(n) gives the number of significant digits of 1/n in factorial base.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of the first 25000 terms (where the color is function of A052126(n))

Wikipedia, Factorial number system (Fractional values)

Index entries for sequences related to factorial base representation

Formula

a(n!)=1 for any n>0.

Example

n     1/n in factorial base           a(n)
--    ----------------------------    ----
1     1                               1
2     0.0 1                           1
3     0.0 0 2                         2
4     0.0 0 1 2                       3
5     0.0 0 1 0 4                     5
6     0.0 0 1                         1
7     0.0 0 0 3 2 0 6                 11
8     0.0 0 0 3                       3
9     0.0 0 0 2 3 2                   7
10    0.0 0 0 2 2                     4
11    0.0 0 0 2 0 5 3 1 4 0 10        25
12    0.0 0 0 2                       2
13    0.0 0 0 1 4 1 2 5 4 8 5 0 12    42
14    0.0 0 0 1 3 3 3                 10
15    0.0 0 0 1 3                     4

Mathematica

f[n_] := Block[{s = 0, r = 1, a = 1/n}, While[a > 0, s += Floor[a]; r++; a = FractionalPart[a]*r]; s] (* after Rémy Sigrist *); Array[f, 70] (* Robert G. Wilson v, Feb 01 2018 *)

Prog

(PARI) {a(n) = my(s=0, r=1, f=1/n); while (f>0, s+= floor(f); r++; f = frac(f)*r); s}

Crossrefs

Cf. A002034, A007623, A034968, A052126.

Sequence in context: A132597 A030335 A256611 * A262215 A030790 A001578

Adjacent sequences: A276347 A276348 A276349 * A276351 A276352 A276353

Keyword

nonn,base

Author

Rémy Sigrist, Dec 12 2016

Status

approved