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

Author

T. D. Noe, Feb 12 2011

Keywords

• nonn
• frac

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.

Examples

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

Links

• 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.

Crossrefs

Cf. A126241 (dropping times).

Formula

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