A297927 Decimal expansion of ratio of number of 1's to number of 2's in A293630.

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?

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

Cf. A293630, A296564.

Sequence in context: A144531 A086357 A138054 * A321873 A218256 A198418

Adjacent sequences: A297924 A297925 A297926 * A297928 A297929 A297930

Keyword

cons,nonn

Author

Iain Fox, Jan 08 2018

Extensions

Terms after a(3) corrected by Iain Fox, Jan 16 2018

Status

approved