A045527 Numbers k such that k! has initial digit '8'.

14, 29, 31, 33, 40, 52, 60, 65, 71, 79, 121, 131, 145, 151, 246, 251, 256, 286, 303, 329, 346, 357, 373, 423, 434, 448, 478, 494, 543, 579, 610, 650, 678, 684, 703, 738, 746, 754, 771, 780, 810, 834, 847

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(9/8) = 0.051152... (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)) = 8. - Amiram Eldar, Jul 17 2020

Example

14 is a term since 14! = 87178291200 has the initial digit 8.

Mathematica

Select[ Range[ 900 ], IntegerDigits[ #! ] [ [1] ] == 8 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 8; \\ 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.

Sequence in context: A325728 A305662 A174070 * A353197 A306212 A041384

Adjacent sequences: A045524 A045525 A045526 * A045528 A045529 A045530

Keyword

nonn,base

Author

Jeff Burch

Status

approved