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%I #31 Dec 04 2020 16:49:47
%S 1,7,1,1,5,25,7,17,19,43,1,13,7,61,1,35,37,79,5,11,23,97,25,53,55,115,
%T 7,31,1,133,17,71,73,151,19,5,41,169,43,89,91,187,1,49,25,205,13,107,
%U 109,223,7,29,59,241,61,125,127,259,1,67,17,277,35,143,145,295,37,19,77,313
%N To get a(n), start with 2n+1, multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.
%C "Start with 2n+1, multiply by 3 and add 1 and divide out any power of 2;" is "equivalent to Start with 3n+2, divide out any power of 2;" - _David A. Corneth_, Aug 22 2020
%H David A. Corneth, <a href="/A102421/b102421.txt">Table of n, a(n) for n = 0..9999</a>
%F a(n) = A337349(2*n+1). - _R. J. Mathar_, Aug 24 2020
%e n=1, 2n+1 = 3 -> 10 -> 5; 5 -> 14 ->7 = a(1).
%e n=17, 2*n+1 = 35 -> 106 ->53; 53 -> 158 -> 79 = a(17).
%p A102421 :=proc(n) local j; j:=3*n+1; while j mod 2 = 0 do j:=j/2; od: j:=3*j-1; while j mod 2 = 0 do j:=j/2; od: j; end proc;
%t nextx[x_Integer] := Block[{ a = x}, a = 3a + 1; While[EvenQ@a, a /= 2]; a = 3a - 1; While[EvenQ@a, a /= 2]; a]; Table[ nextx[2n + 1], {n, 0, 69}] (* _Robert G. Wilson v_ Sep 20 2006 *)
%o (PARI) a(n) = {n = 3*n + 2; n>>=valuation(n, 2); n = 3*n - 1; n >> valuation(n, 2)} \\ _David A. Corneth_, Aug 22 2020
%Y Cf. A000265, A102423.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 15 2006
%E Moved comments to A337349. - _R. J. Mathar_, Aug 24 2020
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