A297890 Decimal expansion of lim_{k->infinity} (A291481(k)^(1/k)).

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

Offset

1,1

Comments

Equals 2^(2 - d) * 3^(d - 1), where d = lim_{k->infinity} (1/k)*Sum_{i=1..k} A293630(i) = 1.275261... (see A296564).

See comments from Jon E. Schoenfield on A296564 for explanation of PARI program.

Is this number transcendental?

Links

Iain Fox, Table of n, a(n) for n = 1..20000

Example

Equals 2.2361513774687490396627784066120440739114649924...
Values evaluated with A291481(k):
  k = 1: 4^(1/1)                 = 4
  k = 2: 7^(1/2)                 = 2.645751311064590590...
  k = 3: 13^(1/3)                = 2.351334687720757489...
  k = 4: 37^(1/4)                = 2.466325714559660444...
  k = 5: 73^(1/5)                = 2.358655818240735626...
  k = 6: 145^(1/6)               = 2.292070651723655173...
  ...
  k = infinity: A291481(k)^(1/k) = 2.236151377468749039...

Prog

(PARI) gen(build) = {
my(S = [1, 2], n = 2, t = 3, L, nPrev, E);
for(j = 1, build, L = S[#S]; n = n*(1+L)-L; t = t*(1+L)-L^2; nPrev = #S; for(r = 1, L, for(i = 1, nPrev-1, S = concat(S, S[i]))));
E = S;
for(j = build + 1, build + #E, L = E[#E+1-(j-build)]; n = n*(1+L)-L; t = t*(1+L)-L^2);
return(2^(2 - t/n)*3^(t/n - 1))
} \\ (gradually increase build to get more precise answers)

Crossrefs

Cf. A291481, A293630, A296564.

Sequence in context: A266583 A002163 A093422 * A083506 A248164 A338993

Adjacent sequences: A297887 A297888 A297889 * A297891 A297892 A297893

Keyword

cons,nonn

Author

Iain Fox, Jan 07 2018

Status

approved