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A297927
Decimal expansion of ratio of number of 1's to number of 2's in A293630.
2
2, 6, 3, 2, 9, 0, 4, 5, 5, 5, 1, 7, 9, 0, 6, 5, 9, 4, 5, 7, 9, 8, 7, 2, 8, 5, 5, 6, 7, 5, 3, 5, 9, 7, 4, 5, 7, 1, 1, 5, 5, 7, 0, 6, 2, 9, 0, 9, 8, 6, 4, 2, 3, 8, 0, 2, 3, 2, 2, 2, 0, 3, 4, 7, 4, 9, 3, 2, 5, 9, 4, 7, 2, 2, 1, 3, 0, 6, 9, 1, 2, 1, 3, 5, 6, 1, 9
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?
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
Sequence in context: A144531 A086357 A138054 * A321873 A218256 A198418
KEYWORD
cons,nonn
AUTHOR
Iain Fox, Jan 08 2018
EXTENSIONS
Terms after a(3) corrected by Iain Fox, Jan 16 2018
STATUS
approved