cp's OEIS Frontend

A136081 Array, read by antidiagonals, numbers with an odd number of 1's in base k expansion.

%I A136081 #10 Sep 21 2015 01:44:05
%S A136081 1,1,3,1,2,5,1,3,4,7,1,4,5,7,9,1,5,6,7,8,11,1,6,7,7,9,11,13,1,7,8,8,9,
%T A136081 11,13,15,1,8,9,9,9,13,13,14,17,1,9,10,10,10,11,16,15,16,19,1,10,11,
%U A136081 11,11,11,16,18,17,19,21,1,11,12,12,12,12,13,21,19,19,21,23,1,12,13,13,13
%N A136081 Array, read by antidiagonals, numbers with an odd number of 1's in base k expansion.
%C A136081 Infinite number of analogs (one per row) of odious numbers.
%F A136081 A(k,n) = n-th number with an odd number of 1's in base k expansion.
%e A136081 The infinite array begins:
%e A136081 ===================================================================
%e A136081 k=?.|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|.n=9.|.n=10.|
%e A136081 k=1.|..1..|..3..|..5..|..7..|..9..|.11..|.13..|.15..|.17..|..19..|A005408
%e A136081 k=2.|..1..|..2..|..4..|..7..|..8..|.11..|.13..|.14..|.16..|..19..|A000069
%e A136081 k=3.|..1..|..3..|..5..|..7..|..9..|.11..|.13..|.15..|.17..|..19..|A005408
%e A136081 k=4.|..1..|..4..|..6..|..7..|..9..|.13..|.16..|.18..|.19..|..21..|new
%e A136081 k=5.|..1..|..5..|..7..|..8..|..9..|.11..|.16..|.21..|.25..|..27..|A137469
%e A136081 k=6.|..1..|..6..|..8..|..9..|.10..|.11..|.13..|.19..|.25..|..31..|A138103
%e A136081 k=7.|..1..|..7..|..9..|.10..|.11..|.12..|.13..|.15..|.22..|..29..|new
%e A136081 k=8.|..1..|..8..|.10..|.11..|.12..|.13..|.14..|.15..|.17..|..25..|new
%e A136081 k=9.|..1..|..9..|.11..|.12..|.13..|.14..|.15..|.16..|.17..|..19..|new
%e A136081 k=10|..1..|.10..|.12..|.13..|.14..|.15..|.16..|.17..|.18..|..19..|new
%e A136081 ===================================================================
%p A136081 od1 := proc(n,k) local ct1,d ; if k = 1 then RETURN( n mod 2 = 1) ; fi ; ct1 := 0 ; for d in convert(n,base,k) do if d = 1 then ct1 := ct1+1 ; fi ; od: RETURN(ct1 mod 2 = 1) ; end: A136081 := proc(k,n) option remember ; local a; if n = 1 then RETURN(1) ; else for a from A136081(k,n-1)+1 do if od1(a,k) then RETURN(a) ; fi ; od: fi ; end: for d from 1 to 15 do for n from 1 to d do printf("%d,", A136081(d+1-n,n)) ; od: od: # _R. J. Mathar_, May 17 2008
%Y A136081 Cf. A000069, A005408, A137469, A138103.
%K A136081 base,easy,nonn,tabl
%O A136081 1,3
%A A136081 _Jonathan Vos Post_, May 10 2008
%E A136081 Corrected and extended by _R. J. Mathar_, May 17 2008