A075477 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+15. Corresponds to selection of every 16th term from A074474.

12, 14, 12, 22, 12, 14, 12, 20, 12, 14, 12, 22, 12, 14, 12, 17, 12, 14, 12, 20, 12, 14, 12, 40, 12, 14, 12, 58, 12, 14, 12, 17, 12, 14, 12, 33, 12, 14, 12, 33, 12, 14, 12, 25, 12, 14, 12, 17, 12, 14, 12, 33, 12, 14, 12, 27, 12, 14, 12, 40, 12, 14, 12, 17, 12, 14, 12, 69, 12

Offset

0,1

Comments

Remark that initial values of 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.

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+15), n=0..256. [corrected by Antti Karttunen, Oct 09 2018]

Example

n=0: 64n+15=15,list={15,46,23,70,35,106,53,160,80,40,20,10..}, i.e. the 12th term is the first that <15, the initial value.

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)));
A075477(n) = A074473((64*n)+15); \\ Antti Karttunen, Oct 09 2018

Crossrefs

Cf. A074473, A074474, A075476-A075482, A006370.

Sequence in context: A042293 A061097 A121288 * A075482 A248019 A275113

Adjacent sequences: A075474 A075475 A075476 * A075478 A075479 A075480

Keyword

nonn

Author

Labos Elemer, Sep 23 2002

Status

approved