A045520 Numbers k such that k! has initial digit '1'.

0, 1, 5, 15, 19, 22, 25, 27, 35, 37, 42, 45, 48, 51, 55, 59, 63, 64, 69, 70, 76, 77, 78, 88, 89, 90, 91, 92, 93, 94, 95, 104, 105, 106, 107, 108, 109, 110, 111, 112, 123, 124, 125, 132, 133, 134, 140, 141, 146, 147, 152, 157, 158, 162, 167, 171, 175, 176, 179, 183

Offset

1,3

Comments

The asymptotic density of this sequence is log_10(2) = 0.301029... (A007524) (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.

Index entries for sequences related to factorial numbers

Formula

A008905(a(n)) = 1. - Amiram Eldar, Jul 17 2020

Example

0 is a term since 0! = 1 has the initial digit 1.

Mathematica

Select[ Range[ 0, 200 ], IntegerDigits[ #! ][ [ 1 ] ] == 1 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 1; \\ Michel Marcus, Feb 07 2017

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045524, A045525, A045526, A045527, A045528, A045529. See also A000142, A007524, A008905.

Sequence in context: A022417 A102180 A365910 * A032472 A290551 A045176

Adjacent sequences: A045517 A045518 A045519 * A045521 A045522 A045523

Keyword

nonn,base

Author

Jeff Burch

Status

approved