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A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1. 1
1, 2, 5, 2, 5, 5, 17, 2, 17, 5, 17, 5, 13, 17, 53, 2, 17, 17, 29, 5, 7, 17, 53, 5, 29, 13, 1619, 17, 29, 53, 1619, 2, 29, 17, 53, 17, 37, 29, 101, 5, 1619, 7, 43, 17, 17, 53, 1619, 5, 37, 29, 29, 13, 53, 1619, 1619, 17, 43, 29, 101, 53, 61, 1619, 1619, 2, 37 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The value 3 cannot appear in this sequence.

The value 1619 appears 1654 times among the first 10000 terms; this is visible as a dashed horizontal line in the corresponding scatterplot.

The most frequent values among the first 10000000 terms are:

  Value     Number of occurences among the first 10000000 terms

  -------   ---------------------------------------------------

   283763   16934

  2017817   15701

     1619   15274

    55667   14706

  2717873    9913

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Ordinal transform of the first 10000000 terms

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

FORMULA

a(n) = A006530(A178168(n)).

a(2*n) = a(n) for any n > 1.

a(2^k) = 2 for any k > 0.

PROG

(PARI) a(n) = my (g=1); while (n>1, my (f=factor(n)); g=max(g, f[#f~, 1]); n=if (n%2, 3*n+1, n/2)); return (g)

CROSSREFS

Cf. A006530, A178168.

Sequence in context: A104289 A177435 A087272 * A107060 A016589 A151572

Adjacent sequences:  A299960 A299961 A299962 * A299964 A299965 A299966

KEYWORD

nonn

AUTHOR

Rémy Sigrist, Feb 22 2018

STATUS

approved

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Last modified February 21 18:45 EST 2019. Contains 320376 sequences. (Running on oeis4.)