cp's OEIS Frontend

A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.

%I A299963 #22 Jul 16 2022 12:33:47
%S A299963 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,
%T A299963 1619,17,29,53,1619,2,29,17,53,17,37,29,101,5,1619,7,43,17,17,53,1619,
%U A299963 5,37,29,29,13,53,1619,1619,17,43,29,101,53,61,1619,1619,2,37
%N A299963 a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.
%C A299963 The value 3 cannot appear in this sequence.
%C A299963 The value 1619 appears 1654 times among the first 10000 terms; this is visible as a dashed horizontal line in the corresponding scatterplot.
%C A299963 The most frequent values among the first 10000000 terms are:
%C A299963 Value     Number of occurrences among the first 10000000 terms
%C A299963   -------   ---------------------------------------------------
%C A299963    283763   16934
%C A299963   2017817   15701
%C A299963      1619   15274
%C A299963     55667   14706
%C A299963   2717873    9913
%H A299963 Rémy Sigrist, <a href="/A299963/b299963.txt">Table of n, a(n) for n = 1..10000</a>
%H A299963 Rémy Sigrist, <a href="/A299963/a299963.png">Ordinal transform of the first 10000000 terms</a>
%H A299963 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A299963 a(n) = A006530(A178168(n)).
%F A299963 a(2*n) = a(n) for any n > 1.
%F A299963 a(2^k) = 2 for any k > 0.
%t A299963 Table[Max[FactorInteger[#][[-1,1]]&/@NestWhileList[If[EvenQ[#],#/2,3#+1]&, n,#>1&]], {n,70}] (* _Harvey P. Dale_, Jun 22 2020 *)
%o A299963 (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)
%Y A299963 Cf. A006530, A055510, A087272, A178168.
%K A299963 nonn
%O A299963 1,2
%A A299963 _Rémy Sigrist_, Feb 22 2018