A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(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

Offset: 1

Author

Rémy Sigrist, Feb 22 2018

Keywords

• nonn

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

Crossrefs

Cf. A006530, A055510, A087272, A178168.

Programs

Mathematica

Table[Max[FactorInteger[#][[-1,1]]&/@NestWhileList[If[EvenQ[#],#/2,3#+1]&, n,#>1&]], {n,70}] (* Harvey P. Dale, Jun 22 2020 *)

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)

Formula

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

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

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