A075480 Number of iteration that first becomes smaller than the initial value if Collatz function (A006370) is iterated, starting with numbers of the form 64n + 39.

14, 69, 48, 20, 14, 27, 17, 33, 14, 20, 22, 40, 14, 58, 20, 17, 14, 33, 22, 33, 14, 64, 17, 33, 14, 71, 20, 35, 14, 40, 43, 17, 14, 71, 71, 25, 14, 27, 17, 40, 14, 22, 25, 27, 14, 43, 25, 17, 14, 66, 27, 25, 14, 76, 17, 20, 14, 22, 43, 27, 14, 66, 25, 17, 14, 22

Offset: 0

Author

Labos Elemer, Sep 23 2002

Keywords

• easy
• nonn

Comments

Initial values of the form 64m + r, if r = {3,11,19,27,35,43,51,55}, provide first-sink-lengths {7,9,7,9,7,9,7,9} respectively; e.g., {64k + 19, 192k + 58, 96k + 29, 288k + 88, 144k + 44, 72k + 22, 36k + 11} submerge first below initial value at the 7th term, 36k + 11 < 64k + 19.

Examples

			n=0: 64n + 39 = 39, Collatz trajectory = {39, 118, 59, 178, 89, 268, 134, 67, 202, 101, 304, 152, 76, 38, 19, 58, ....}, i.e., the 14th term = 38 is the first that is less than 39, the initial value, so a(0)=14.
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A074473, A074474, A075476-A075483, A006370.

Programs

Maple

col := proc(n) if(n mod 2 = 0)then return n/2: fi: return 3*n+1: end: A075480 := proc(n) local s,v: s:=1: v:=64*n+39: while v>=64*n+39 do v:=col(v): s:=s+1: od: return s: end: seq(A075480(n),n=0..65); # Nathaniel Johnston, Jun 22 2011

Formula

a(n) = A074473(64n+39).

Extensions

Keyword:fini removed by Nathaniel Johnston, Jun 23 2011

Edited by Jon E. Schoenfield, Feb 23 2019