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A045524
Numbers k such that k! has initial digit '5'.
18
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
Sharon Kunoff, N! has the first digit property, The Fibonacci Quarterly, Vol. 25, No. 4 (1987), pp. 365-367.
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.
Sequence in context: A208543 A009475 A063292 * A125228 A024837 A205864
KEYWORD
nonn,base
AUTHOR
STATUS
approved