A165342 a(n) = A061037(n+2)/A000265(n+4).

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, 56, 29, 15, 31, 8, 33, 17, 35, 18, 37, 19, 39, 10, 41, 21, 43, 44, 45, 23, 47, 12, 49, 25, 51, 26, 53, 27, 55, 14, 57, 29, 59, 240, 61, 31, 63, 16, 65, 33, 67, 34, 69, 35, 71, 18, 73, 37

Offset: 0

Author

Paul Curtz, Sep 15 2009

Keywords

• nonn

Comments

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

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000

Programs

Maple

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

Mathematica

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 *)

Extensions

Edited, extended by R. J. Mathar, Sep 16 2009