

A218802


Decimal expansion of largest x such that x^2 = Gamma(x+1).


2



3, 5, 6, 2, 3, 8, 2, 2, 8, 5, 3, 9, 0, 8, 9, 7, 6, 9, 1, 4, 1, 5, 6, 4, 4, 3, 4, 2, 7, 4, 7, 6, 1, 0, 3, 1, 1, 7, 8, 1, 1, 0, 6, 4, 7, 5, 0, 9, 7, 2, 1, 6, 1, 9, 4, 3, 3, 7, 9, 2, 0, 3, 1, 1, 7, 0, 0, 5, 4, 1, 6, 7, 6, 5, 0, 8, 5, 5, 6, 5, 6, 0, 2, 6, 5, 4, 7, 6, 3, 8, 8, 6, 4, 5, 0, 9, 2, 4, 0, 2, 3, 6, 0, 2, 6, 3, 7
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OFFSET

1,1


COMMENTS

In other words, the largest number whose square and factorial coincide.
As one knows from the famous illustration in Jahnke and Emde (p. 13) (or Abramowitz and Stegun, p. 255), there are infinitely many solutions to x^2 = x!. For example, there is another solution near 1.8065.  N. J. A. Sloane, Dec 24 2012
Decimal expansion of greatest real fixed point of Gamma(x). (The only other positive fixed point is 1.)  Rick L. Shepherd, Feb 24 2014


REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 255.
Eugene Jahnke and Fritz Emde, Table of Functions with Formulae and Curves, Dover Book, New York, 1945, page 13.


LINKS

Table of n, a(n) for n=1..107.


EXAMPLE

3.562382285390897691415...


MAPLE

Digits:= 150:
s:= convert(fsolve(x^2 = GAMMA(x+1), x=7/2)/10, string):
seq(parse(s[n+1]), n=1..120); # Alois P. Heinz, Dec 26 2012


MATHEMATICA

RealDigits[x /. FindRoot[x^2 == Gamma[x + 1], {x, 3}, WorkingPrecision > 100]][[1]] (* Bruno Berselli, Dec 24 2012 *)


PROG

(PARI) solve(x=3, 4, x^2gamma(x+1)) \\ Charles R Greathouse IV, Dec 26 2012
(PARI) solve(x=3, 4, xgamma(x)) \\ Rick L. Shepherd, Feb 24 2014


CROSSREFS

Sequence in context: A178255 A154467 A152713 * A236101 A203802 A306554
Adjacent sequences: A218799 A218800 A218801 * A218803 A218804 A218805


KEYWORD

nonn,cons


AUTHOR

Marshes Skutnik, Nov 06 2012


STATUS

approved



