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A075476 Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of form 64n+7. Corresponds to selection of every 16th term from A074474. 10
12, 84, 12, 14, 12, 35, 12, 14, 12, 17, 12, 14, 12, 25, 12, 14, 12, 25, 12, 14, 12, 27, 12, 14, 12, 17, 12, 14, 12, 38, 12, 14, 12, 25, 12, 14, 12, 45, 12, 14, 12, 17, 12, 14, 12, 27, 12, 14, 12, 20, 12, 14, 12, 79, 12, 14, 12, 17, 12, 14, 12, 20, 12, 14, 12, 33, 12, 14, 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+7), n=0, ..., 256

EXAMPLE

n=0: 64n+7=7, list={7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5..}, i.e. the 12th term is the first that <12, the initial value.

MATHEMATICA

lcoll[n_] := Length[NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # >= n &]]; Table[lcoll[64*i + 7], {i, 0, 68}] (* Jayanta Basu, Jun 15 2013 *)

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)));

A075476(n) = A074473((64*n)+7); \\ Antti Karttunen, Oct 09 2018

CROSSREFS

Cf. A074473, A074474, A006370.

Sequence in context: A026949 A165127 A213347 * A298977 A213784 A085409

Adjacent sequences:  A075473 A075474 A075475 * A075477 A075478 A075479

KEYWORD

nonn

AUTHOR

Labos Elemer, Sep 23 2002

EXTENSIONS

Typo in formula corrected by Antti Karttunen, Oct 09 2018

STATUS

approved

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Last modified January 21 19:52 EST 2019. Contains 319350 sequences. (Running on oeis4.)