A296301 Decimal expansion of Product_{k>=2} k^(1/k!).

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

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Eric Weisstein's World of Mathematics, Nested Radical

Eric Weisstein's World of Mathematics, Somos's Quadratic Recurrence Constant

Formula

Equals (2*(3*(4*(5*(6*(7*...)^(1/7))^(1/6))^(1/5))^(1/4))^(1/3))^(1/2).

Equals exp(Sum_{k>=2} log(k)/k!).

Equals lim_{k->infinity} b(k)^(1/k!), where b(k) = k*b(k-1)^k with b(0) = 1.

Equals Product_{p prime} p^(Sum_{k>=2} (p-adic valuation of k)/k!).

Example

1.8290246795635718643895723573648858491007676333721141167306441...

Mathematica

RealDigits[Exp[Sum[ Log[k]/k!, {k, 2, 700}]], 10, 100][[1]] (* G. C. Greubel, Jul 28 2018 *)

Prog

(PARI) exp(suminf(k=2, log(k)/k!)) \\ Michel Marcus, Dec 11 2017

Crossrefs

Cf. A112302, A115522, A123852, A188835, A259235.

Sequence in context: A278809 A306617 A278261 * A019865 A198993 A307565

Adjacent sequences: A296298 A296299 A296300 * A296302 A296303 A296304

Keyword

nonn,cons

Author

Ilya Gutkovskiy, Dec 09 2017

Status

approved