A045528 Numbers k such that k! has initial digit '9'.

96, 97, 98, 99, 100, 101, 102, 103, 122, 139, 166, 190, 233, 241, 261, 268, 301, 331, 366, 380, 415, 431, 445, 481, 497, 514, 521, 583, 596, 624, 629, 634, 655, 672, 690, 716, 723, 762, 789, 799, 821, 833, 861, 897

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(10/9) = 1 - log_10(9) = 0.045757... (A104140) (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)) = 9. - Amiram Eldar, Jul 17 2020

Example

96 is a term since 96! = 9.916779... * 10^149 has the initial digit 9.

Mathematica

Select[ Range[ 900 ], IntegerDigits[ #! ] [ [1] ] == 9 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 9; \\ Michel Marcus, Feb 08 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, A008905, A104140.

Sequence in context: A050277 A090221 A334654 * A181470 A306104 A257411

Adjacent sequences: A045525 A045526 A045527 * A045529 A045530 A045531

Keyword

nonn,base

Author

Jeff Burch

Extensions

More terms from Robert G. Wilson v, Jan 03 2001

Status

approved