A165342 - OEIS

%I #22 Sep 20 2018 00:34:51

%S 0,1,1,3,2,5,3,7,2,9,5,11,12,13,7,15,4,17,9,19,10,21,11,23,6,25,13,27,

%T 56,29,15,31,8,33,17,35,18,37,19,39,10,41,21,43,44,45,23,47,12,49,25,

%U 51,26,53,27,55,14,57,29,59,240,61,31,63,16,65,33,67,34,69,35,71,18,73,37

%N a(n) = A061037(n+2)/A000265(n+4).

%C Coincides with A026741 at many places. Apparently the ratio between the two sequences is always one of 1/2, 1, 2, 4, 8, 16, ...

%C The distance between antecedents of 1 is 1, between antecedents of 3 is 3, and more generally, for 1+2*k this distance is 1+2*k. Their respective ranks are 1,2,3,5,6,7,9,10,11,... (A042968). - _Paul Curtz_, Apr 08 2011

%H G. C. Greubel, <a href="/A165342/b165342.txt">Table of n, a(n) for n = 0..10000</a>

%p A000265 := proc(n) nshft := n ; while nshft mod 2 = 0 do nshft := nshft/2 ; od: nshft ; end:

%p A061037 := proc(n) numer ( 1/4-1/n^2) ; end: A165342 := proc(n) A061037(n+2)/A000265(n+4) ; end: seq( A165342(n),n=0..120) ; # _R. J. Mathar_, Sep 16 2009

%t A061037[n_] := Numerator[(n - 2) (n + 2)/(4 n^2)]; A000265[n_] := If[n == 0, 0, n/2^IntegerExponent[n, 2]]; Table[A061037[n + 2]/A000265[n + 4], {n, 0, 100}] (* _G. C. Greubel_, Sep 19 2018 *)

%K nonn

%O 0,4

%A _Paul Curtz_, Sep 15 2009

%E Edited, extended by _R. J. Mathar_, Sep 16 2009