A045524 Numbers k such that k! has initial digit '5'.

7, 21, 38, 46, 61, 66, 81, 119, 137, 144, 150, 165, 189, 196, 206, 209, 221, 224, 235, 243, 248, 253, 258, 279, 292, 340, 342, 353, 362, 383, 413, 429, 440, 488, 508, 529, 540, 584, 597, 611, 630, 651, 662, 679, 685, 704, 711, 718, 725, 732, 764, 782, 812

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base

Comments

n such that A000030(A000142(n)) = 5. - Robert Israel, Feb 07 2017

The asymptotic density of this sequence is log_10(6/5) = 0.079181... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020

Examples

			7 is a term since 7! = 5040 has the initial digit 5.
		

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

Crossrefs

For factorials with initial digit d (1 <= d <= 9) see A045509, A045510, A045511, A045516, A045517, A045518, A282021, A045519; A045520, A045521, A045522, A045523, A045525, A045526, A045527, A045528, A045529.

Cf. A000030, A000142, A008905.

Programs

Maple

filter:= proc(t) local tf;
tf:= t!;
floor(tf/10^ilog10(tf)) = 5
end proc:
select(filter, [$1..1000]); # Robert Israel, Feb 07 2017

Mathematica

Select[ Range[ 850 ], IntegerDigits[ #! ] [[1]] == 5 & ]

PARI

isok(n) = digits(n!)[1] == 5; \\ Michel Marcus, Feb 08 2017

Formula

A008905(a(n)) = 5. - Amiram Eldar, Jul 17 2020