A129624 - OEIS

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A129624

Decimal expansion of the constant x satisfying x! = Gamma(x+1) = 40.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Solutions were provided by Bob Hanlon and Peter Pein.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

4.331292424499713465838941491042338081138561546026782297287499557485752...

MAPLE

read("transforms3") ; Digits := 120 ; x := 4.0 ; for l from 1 to 10 do x := x-(1-40/GAMMA(x+1))/Psi(x+1) ; x := evalf(x) ; end do; CONSTTOLIST(x) ; # R. J. Mathar, Mar 23 2010

MATHEMATICA

FindRoot[(x + 1)! == 40, {x, 4, 5}, WorkingPrecision -> 50]( * Bob Hanlon (hanlonr(AT)cox.net) and Peter Pein, edited by M. F. Hasler, Jun 16 2024 *)

PROG

(PARI) A129624_first(N=99, t=40, L=log(t)*.55)=localprec(N+5); digits(solve(x=L+1.5, L+2.5, gamma(x+1)-t)\10^-N) \\ M. F. Hasler, Jun 13 2024

CROSSREFS

Similar for x! = n: A319275 (n=3), A319276 (n=4), A319277 (n=5).

Sequence in context: A060997 A177270 A177160 * A177038 A019975 A327869

Adjacent sequences: A129621 A129622 A129623 * A129625 A129626 A129627

KEYWORD

nonn,cons

AUTHOR

Roger L. Bagula, May 30 2007

EXTENSIONS

More digits from R. J. Mathar, Mar 23 2010

STATUS

approved