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A129624 Decimal expansion of the constant x satisfying x! = Gamma[x+1] = 40. 3
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

From symmetrical groups associated with exceptional groups: in this case the exceptional group now called E7.5. I call the symmetrical group S4_q. Solutions were provided in my egroup by Bob Hanlon and Peter Pein.

LINKS

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

FORMULA

a(n) = nth_Digits[4.3312924244997134658389414910423380811385615460267822972874964374249]

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

(* Bob Hanlon (hanlonr(AT)cox.net): Solve is not intended for much beyond polynomial equations.Use FindRoot*) FindRoot[(4 + q)! - 40 == 0, {q, 0.5}] {q -> 0.3312924244997131`} FindRoot[Gamma[5 + q] - 40 == 0, {q, 0.5}] {q -> 0.3312924244997131`} (* Peter Pein : use the function FindRoot to get the zeros of transcendental functions :*) FindRoot[Gamma[5 + x] == 40, {x, 0, 1}, WorkingPrecision -> 50] {x -> 0.3312924244997134658389414910423380811385615460267822972874964374249` 49.99999999999999} FindRoot[(x + 4)! == 40, {x, 0, 1}, WorkingPrecision -> 50] {x -> 0.3312924244997134658389414910423380811385615460267822972874964374249` 49.99999999999999} (* digits from*) a = 0.3312924244997134658389414910423380811385615460267822972874964374249; Flatten[Join[{{4}}, Table[Mod[Floor[10^n*a], 10], {n, 1, 50}]]]

CROSSREFS

Sequence in context: A060997 A177270 A177160 * A177038 A019975 A196274

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

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)