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A270968 Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.

%I A270968 #9 Apr 09 2016 17:45:18
%S A270968 3,1,13,9,23,7,33,19,43,3,53,29,63,17,73,39,83,11,93,49,103,27,113,59,
%T A270968 123,1,133,69,143,37,153,79,163,21,173,89,183,47,193,99,203,13,213,
%U A270968 109,223,57,233,119,243,31,253,129,263,67,273,139,283,9,293,149,303
%N A270968 Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.
%C A270968 The odd-indexed terms a(2i+1) = 10i+3 = A017305(i), i>=0;
%C A270968 a(4i+4) = 10i+9 = A017377(i), i>=0;
%C A270968 a(8i+6) = 10i+7 = A017353(i), i>=0;
%C A270968 a(16i+2) = 10i+1 = A017281(i), i>=0.
%C A270968 Note that a(n) = a(16n-6) = a(6n-2)/3. No multiple of 5 is in this sequence.
%C A270968 a(n) = R(2n-1) < 2n-1 for n = 2, 6, 10, ..., 2+4i,...
%F A270968 a(n) = A000265(A017341(n-1)). - _Michel Marcus_, Mar 27 2016
%e A270968 a(4)=9 because (2*4-1) = 7  -> (5*7+1)/2^2 = 9.
%t A270968 nextOddK[n_] := Module[{m=5n+1}, While[EvenQ[m], m=m/2]; m]; (* assumes odd n *) Table[nextOddK[n], {n, 1, 200, 2}]
%o A270968 (PARI) a(n) = my(m = 2*n-1, c = 5*m+1); c/2^valuation(c, 2); \\ _Michel Marcus_, Mar 27 2016
%Y A270968 Cf. A075677, A017281, A017305, A017353, A017377, A133423, A133424, A174795, A133419, A133420, A232711, A259207, A267969.
%K A270968 nonn,easy
%O A270968 1,1
%A A270968 _Michel Lagneau_, Mar 27 2016