A045526 Numbers k such that k! has initial digit '7'.

6, 56, 80, 156, 161, 170, 186, 200, 230, 238, 277, 288, 305, 307, 323, 325, 327, 344, 385, 410, 451, 454, 472, 475, 504, 532, 547, 551, 575, 592, 601, 615, 645, 661, 697, 710, 724, 731, 790, 800, 811, 822, 848

Offset

1,1

Comments

The asymptotic density of this sequence is log_10(8/7) = 0.057991... (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)) = 7. - Amiram Eldar, Jul 17 2020

Example

6 is a term since 6! = 720 has the initial digit 7.

Mathematica

Select[ Range[ 900 ], IntegerDigits[ #! ] [[1]] == 7 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 7; \\ 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: A335217 A335199 A137033 * A164579 A137034 A177059

Adjacent sequences: A045523 A045524 A045525 * A045527 A045528 A045529

Keyword

nonn,base

Author

Jeff Burch

Status

approved