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A216377 The most significant digit in base n representation of n!. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A300823 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

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Last modified April 21 07:53 EDT 2019. Contains 322327 sequences. (Running on oeis4.)