

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
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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 occurrences 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: A309697 A177435 A087272 * A107060 A016589 A151572
Adjacent sequences: A299960 A299961 A299962 * A299964 A299965 A299966


KEYWORD

nonn


AUTHOR

Rémy Sigrist, Feb 22 2018


STATUS

approved



