cp's OEIS Frontend

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

%I A297927 #10 Jan 16 2018 20:49:58
%S A297927 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,
%T A297927 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,
%U A297927 5,9,4,7,2,2,1,3,0,6,9,1,2,1,3,5,6,1,9
%N A297927 Decimal expansion of ratio of number of 1's to number of 2's in A293630.
%C A297927 Equals (2 - d)/(d - 1), where d = lim_{k->infinity} (1/k)*Sum_{i=1..k} A293630(i) = 1.275261... (see A296564).
%C A297927 See comments from _Jon E. Schoenfield_ on A296564 for explanation of PARI program.
%C A297927 Is this number transcendental?
%H A297927 Iain Fox, <a href="/A297927/b297927.txt">Table of n, a(n) for n = 1..20000</a>
%e A297927 Equals 2.6329045551790659457987285567535974571155706290...
%e A297927 After generating k steps of A293630:
%e A297927   k = 0:        [1, 2];                  1
%e A297927   k = 1:        [1, 2, 1, 1];            3
%e A297927   k = 2:        [1, 2, 1, 1, 1, 2, 1];   2.5
%e A297927   k = 3:        [1, 2, 1, 1, 1, 2, ...]; 2.25
%e A297927   k = 4:        [1, 2, 1, 1, 1, 2, ...]; 2.7
%e A297927   k = 5:        [1, 2, 1, 1, 1, 2, ...]; 2.65
%e A297927   k = 6:        [1, 2, 1, 1, 1, 2, ...]; 2.625
%e A297927   ...
%e A297927   k = infinity: [1, 2, 1, 1, 1, 2, ...]; 2.632904555179...
%o A297927 (PARI) gen(build) = {
%o A297927 my(S = [1, 2], n = 2, t = 3, L, nPrev, E);
%o A297927 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]))));
%o A297927 E = S;
%o A297927 for(j = build + 1, build + #E, L = E[#E+1-(j-build)]; n = n*(1+L)-L; t = t*(1+L)-L^2);
%o A297927 return(1.0*(2 - t/n)/(t/n - 1))
%o A297927 } \\ (gradually increase build to get more precise answers)
%Y A297927 Cf. A293630, A296564.
%K A297927 cons,nonn
%O A297927 1,1
%A A297927 _Iain Fox_, Jan 08 2018
%E A297927 Terms after a(3) corrected by _Iain Fox_, Jan 16 2018