A216377 The most significant digit in base n representation of n!.

1, 2, 1, 4, 3, 2, 1, 6, 3, 2, 1, 7, 4, 2, 1, 10, 5, 2, 1, 15, 8, 4, 2, 1, 13, 6, 3, 1, 25, 12, 6, 3, 1, 25, 12, 6, 3, 1, 28, 13, 6, 3, 1, 33, 16, 7, 3, 1, 41, 20, 9, 4, 2, 1, 26, 12, 6, 2, 1, 38, 18, 8, 3, 1, 57, 27, 12, 5, 2, 1, 43, 20, 9, 4, 2, 72, 33, 15, 7, 3, 1

Offset

2,2

Comments

a(n) < n, by definition.

Numbers n such that a(n)=1: 2, 4, 8, 12, 16, 20, 25, 29, 34, 39, 44, 49, 55, 60, 65, 71, 82, 88, 94, 105, 111, 117, 123, 136, ... (see A221707).

Numbers n such that a(n) > a(k) for k < n: 2, 3, 5, 9, 13, 17, 21, 30, 40, 45, 50, 66, 77, 100, 118, 124, 130, 155, 161, 226, 246, 273, 371, 378, 385, 421, 450, 472, 509, 584, 599, 637, 660, 683, 745, 784, 855, 983, 991, 999, ... (see A221708).

Links

Alois P. Heinz, Table of n, a(n) for n = 2..10000

Formula

a(n) = modlg(n!, n), where modlg is the function defined in A215894: modlg(A,B) = floor(A / B^floor(logB(A))), logB is the logarithm base B.

Maple

a:= n-> iquo(n!, n^ilog[n](n!)):
seq(a(n), n=2..100);  # Alois P. Heinz, Sep 06 2012

Mathematica

Table[IntegerDigits[n!, n][[1]], {n, 2, 100}] (* T. D. Noe, Sep 06 2012 *)

Prog

(Python)
import math
def modlg(a, b):
    return a // b**int(math.log(a, b))
for n in range(2, 88):
    print modlg(math.factorial(n), n),

Crossrefs

Cf. A216021, A215894, A221707, A221708.

Cf. also to scatter plots of A265891 and A265894.

Sequence in context: A345942 A175702 A303781 * A253515 A319521 A281589

Adjacent sequences: A216374 A216375 A216376 * A216378 A216379 A216380

Keyword

nonn,base,look

Author

Alex Ratushnyak, Sep 06 2012

Status

approved