A186109 Numerator of the cumulative frequency of the dropping time in the Collatz iteration.

1, 3, 13, 7, 115, 237, 15, 1935, 7825, 31473, 31711, 254649, 15957, 2050541, 8219801, 16490635, 33035745, 132455435, 530485275, 1061920785, 4253619813, 4256987887, 34095896991, 136471574881, 273072139013, 136638599097, 2187167322891, 4377196161075, 4378797345767, 35049397190341

Offset

1,2

Comments

The possible dropping times are in A020914. The denominators are in A186110. The frequency of the n-th dropping time is A186107(n)/A186108(n).

Riho Terras' classic paper about the Collatz problem shows the decimal values of 2(1-c(k)) in Table A, where c(k) is the cumulative frequency of dropping times <= k.

Links

Table of n, a(n) for n=1..30.

Index entries for sequences related to 3x+1 (or Collatz) problem

Riho Terras, A stopping time problem on the positive integers, ACTA Arith. 30 (1976), 241-252.

Formula

a(n) = numerator of Sum_{k=1..n} A186009(k) / 2^A020914(k-1).

Example

The cumulative frequencies are 1/2, 3/4, 13/16, 7/8, 115/128, 237/256, 15/16, 1935/2048, 7825/8192, ... .

Crossrefs

Cf. A126241 (dropping times).

Sequence in context: A140445 A320039 A242173 * A012789 A273025 A273122

Adjacent sequences: A186106 A186107 A186108 * A186110 A186111 A186112

Keyword

nonn,frac

Author

T. D. Noe, Feb 12 2011

Status

approved