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A373730 Reduced Collatz function R applied to the numbers 6n+1: a(n) = R(6n+1), where R(k) = (3k+1)/2^r, with r as large as possible.

%I A373730 #31 Aug 19 2024 11:42:30
%S A373730 1,11,5,29,19,47,7,65,37,83,23,101,55,119,1,137,73,155,41,173,91,191,
%T A373730 25,209,109,227,59,245,127,263,17,281,145,299,77,317,163,335,43,353,
%U A373730 181,371,95,389,199,407,13,425,217,443,113,461,235,479,61,497,253,515
%N A373730 Reduced Collatz function R applied to the numbers 6n+1: a(n) = R(6n+1), where R(k) = (3k+1)/2^r, with r as large as possible.
%H A373730 Paolo Xausa, <a href="/A373730/b373730.txt">Table of n, a(n) for n = 0..10000</a>
%F A373730 a(n) = A000265(A017185(n)).
%t A373730 A373730[n_] := #/2^IntegerExponent[#, 2] & [9*n + 2];
%t A373730 Array[A373730, 100, 0] (* _Paolo Xausa_, Aug 19 2024 *)
%o A373730 (PARI) a(n) = n=9*n+2; n>>valuation(n,2);
%Y A373730 Cf. A000265, A017185, A075677, A260658.
%K A373730 nonn,easy
%O A373730 0,2
%A A373730 _Jonas Kaiser_, Jun 17 2024