A075482 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of the form 64n + 59.

12, 14, 12, 45, 12, 14, 12, 17, 12, 14, 12, 33, 12, 14, 12, 20, 12, 14, 12, 25, 12, 14, 12, 17, 12, 14, 12, 20, 12, 14, 12, 30, 12, 14, 12, 25, 12, 14, 12, 17, 12, 14, 12, 30, 12, 14, 12, 22, 12, 14, 12, 69, 12, 14, 12, 17, 12, 14, 12, 22, 12, 14, 12, 22, 12, 14, 12, 82, 12

Offset

0,1

Comments

1stSubmergeLengths[=A074473] with initial values belonging to other residue classes modulo 64 are either listed in A075476-A075483 or can be easily determined. For 64k+2s the first sink below initial value is at 2nd iterate; for 64k+4s+1 the first submerge below initial value comes at 4th term of iteration list; finally if initial value is of 64k+4s+3 form or moreover initial value = 64k+r, r = 3, 11, 19, 23, 35, 43, 51, 55, then for all k first sink emerges at the 7th, 9th, 7th, 9th, 7th, 9th, 7th, 9th iterates, respectively.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

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

Formula

a(n) = A074473(64n + 59).

Example

n=0: 64n + 59 = 59, the list = {59,178,89,268,134,67,202,101,304,152,76,38,...} the 12th term = 38 < 59 = the initial value, so a(0)=12.

Mathematica

Table[Function[m, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, m, # >= m - 1 &]][64 n + 59], {n, 0, 84}] (* Michael De Vlieger, Mar 25 2017 *)

Prog

(PARI)
A006370(n) = if(n%2, 3*n+1, n/2);
A074473(n) = if(1==n, n, my(org_n=n); for(i=1, oo, if(n<org_n, return(i)); n = A006370(n)));
A075482(n) = A074473((64*n)+59); \\ Antti Karttunen, Oct 09 2018

Crossrefs

Cf. A006370, A074472, A074473, A075476, A075477-A075483.

Sequence in context: A061097 A121288 A075477 * A248019 A275113 A043651

Adjacent sequences: A075479 A075480 A075481 * A075483 A075484 A075485

Keyword

nonn

Author

Labos Elemer, Sep 24 2002

Status

approved