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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 19 10:30 EDT 2021. Contains 343112 sequences. (Running on oeis4.)