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A006488 Numbers n such that n! has a square number of digits.
(Formerly M0830)
3
0, 1, 2, 3, 7, 12, 18, 32, 59, 81, 105, 132, 228, 265, 284, 304, 367, 389, 435, 483, 508, 697, 726, 944, 1011, 1045, 1080, 1115, 1187, 1454, 1494, 1617, 1659, 1788, 1921, 2012, 2105, 2200, 2248, 2395, 2445, 2861, 2915, 3192, 3480, 3539, 3902, 3964, 4476 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers whose square is represented by the number of digits of n!: 1, 2, 3, 4, 6, 9, 11, 13, 15, 21, 23, 24, 25, 28, 29, ..., . - Robert G. Wilson v, May 14 2014

REFERENCES

M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 55.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 0..1310

Eric Weisstein's World of Mathematics, Stirling's Approximation

Eric Weisstein's World of Mathematics, Stirling's Series

Index entries for sequences related to factorial numbers

MATHEMATICA

LogBase10Stirling[n_] := Floor[Log[10, 2 Pi n]/2 + n*Log[10, n/E] + Log[10, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)]]; Select[ Range[ 4500], IntegerQ[ Sqrt[ (LogBase10Stirling[ # ] + 1)]] & ] (* The Mathematica coding comes from J. Stirling's expansion for the Gamma function; see the links. For more terms inside the last Log_10 function, use A001163 & A001164. Robert G. Wilson v, Apr 27 2014 *)

PROG

(PARI) isok(n) = issquare(#Str(n!)); \\ Michel Marcus, Sep 05 2015

CROSSREFS

Cf. A000142, A056851.

Sequence in context: A049623 A228828 A061577 * A121430 A217379 A023606

Adjacent sequences:  A006485 A006486 A006487 * A006489 A006490 A006491

KEYWORD

nonn,base

AUTHOR

N. J. A. Sloane and Robert G. Wilson v

STATUS

approved

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Last modified April 29 01:04 EDT 2017. Contains 285604 sequences.