OFFSET
1,1
COMMENTS
Equals (2 - d)/(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 2.6329045551790659457987285567535974571155706290...
After generating k steps of A293630:
k = 0: [1, 2]; 1
k = 1: [1, 2, 1, 1]; 3
k = 2: [1, 2, 1, 1, 1, 2, 1]; 2.5
k = 3: [1, 2, 1, 1, 1, 2, ...]; 2.25
k = 4: [1, 2, 1, 1, 1, 2, ...]; 2.7
k = 5: [1, 2, 1, 1, 1, 2, ...]; 2.65
k = 6: [1, 2, 1, 1, 1, 2, ...]; 2.625
...
k = infinity: [1, 2, 1, 1, 1, 2, ...]; 2.632904555179...
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(1.0*(2 - t/n)/(t/n - 1))
} \\ (gradually increase build to get more precise answers)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Iain Fox, Jan 08 2018
EXTENSIONS
Terms after a(3) corrected by Iain Fox, Jan 16 2018
STATUS
approved