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
Examples
1.8290246795635718643895723573648858491007676333721141167306441...
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
Programs
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Mathematica
RealDigits[Exp[Sum[ Log[k]/k!, {k, 2, 700}]], 10, 100][[1]] (* G. C. Greubel, Jul 28 2018 *) -
PARI
exp(suminf(k=2, log(k)/k!)) \\ Michel Marcus, Dec 11 2017
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!).