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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The asymptotic density of this sequence is log_10(6/5) = 0.079181... (Kunoff, 1987). - Amiram Eldar, Jul 17 2020 REFERENCES n such that A000030(A000142(n))=5. Robert Israel, Feb 07 2017 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. 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 STATUS approved

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Last modified October 27 06:09 EDT 2020. Contains 338035 sequences. (Running on oeis4.)