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

Author

Iain Fox, Jan 08 2018

Keywords

• cons
• nonn

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?

Examples

			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...
		

Links

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

Crossrefs

Cf. A293630, A296564.

Programs

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)

Extensions

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