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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
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
FORMULA
a(n) = A006530(A178168(n)).
a(2*n) = a(n) for any n > 1.
a(2^k) = 2 for any k > 0.
MATHEMATICA
Table[Max[FactorInteger[#][[-1, 1]]&/@NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], {n, 70}] (* Harvey P. Dale, Jun 22 2020 *)
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Feb 22 2018
STATUS
approved