A045523 Numbers k such that k! has initial digit '4'.

8, 12, 26, 53, 57, 73, 82, 118, 129, 155, 160, 169, 185, 212, 215, 218, 232, 240, 265, 272, 281, 294, 338, 351, 369, 376, 388, 393, 398, 403, 408, 421, 432, 443, 446, 482, 485, 498, 515, 522, 533, 544, 548, 576, 580, 593, 602, 616, 621, 641, 646, 657, 668

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(5/4) = 0.096910... (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)) = 4. - Amiram Eldar, Jul 17 2020

Example

8 is a term since 8! = 40320 has the initial digit 4.

Mathematica

Select[ Range[ 700 ], IntegerDigits[ #! ] [[ 1 ]] == 4 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 4; \\ 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, A008905.

Sequence in context: A367894 A210982 A067677 * A006983 A283148 A072327

Adjacent sequences: A045520 A045521 A045522 * A045524 A045525 A045526

Keyword

nonn,base

Author

Jeff Burch

Status

approved