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

1,1

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

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)) = 5. - Amiram Eldar, Jul 17 2020

Example

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

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 & ]

Prog

(PARI) isok(n) = digits(n!)[1] == 5; \\ 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, A045525, A045526, A045527, A045528, A045529.

Cf. A000030, A000142, A008905.

Sequence in context: A208543 A009475 A063292 * A125228 A024837 A205864

Adjacent sequences: A045521 A045522 A045523 * A045525 A045526 A045527

Keyword

nonn,base

Author

Jeff Burch

Status

approved