A221708 -id:A221708 - cp's OEIS frontend

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

Alex Ratushnyak, Sep 06 2012

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).

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

Cf. A216021, A215894, A221707, A221708.

Cf. also to scatter plots of A265891 and A265894.

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

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

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), end=', ')

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.

A221707 Numbers n such that A216377(n) = 1.

Original entry on oeis.org

2, 4, 8, 12, 16, 20, 25, 29, 34, 39, 44, 49, 55, 60, 65, 71, 82, 88, 94, 105, 111, 117, 123, 136, 142, 148, 154, 167, 173, 180, 186, 193, 199, 206, 212, 219, 225, 232, 239, 252, 259, 266, 279, 286, 293, 300, 307, 314, 321, 328, 335, 342, 349, 356, 363, 370

Offset: 1

N. J. A. Sloane, Jan 25 2013

nonn

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Cf. A216377, A221708.

Select[Range[2,400],IntegerDigits[#!,#][[1]]==1&] (* Harvey P. Dale, Aug 14 2020 *)

More terms from Alois P. Heinz, Jan 28 2013

cp's OEIS Frontend

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

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