A045525 Numbers k such that k! has initial digit '6'.

3, 13, 18, 24, 43, 49, 72, 120, 130, 138, 174, 178, 182, 193, 203, 227, 263, 270, 290, 309, 311, 313, 315, 317, 319, 321, 355, 364, 371, 378, 390, 395, 400, 405, 418, 426, 437, 457, 460, 463, 466, 469, 491, 501, 511, 518, 525, 536, 555, 559, 563, 567, 571

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(7/6) = 0.066946... (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)) = 6. - Amiram Eldar, Jul 17 2020

Example

3 is a term since 3! = 6 has the initial digit 6.

Mathematica

Select[ Range[ 600 ], IntegerDigits[ #! ] [ [1] ] == 6 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 6; \\ 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: A273946 A070518 A263182 * A030774 A024685 A024474

Adjacent sequences: A045522 A045523 A045524 * A045526 A045527 A045528

Keyword

nonn,base

Author

Jeff Burch

Status

approved