A136081 Array, read by antidiagonals, numbers with an odd number of 1's in base k expansion.
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, 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, 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
Offset: 1
Examples
The infinite array begins: =================================================================== k=?.|.n=1.|.n=2.|.n=3.|.n=4.|.n=5.|.n=6.|.n=7.|.n=8.|.n=9.|.n=10.| k=1.|..1..|..3..|..5..|..7..|..9..|.11..|.13..|.15..|.17..|..19..|A005408 k=2.|..1..|..2..|..4..|..7..|..8..|.11..|.13..|.14..|.16..|..19..|A000069 k=3.|..1..|..3..|..5..|..7..|..9..|.11..|.13..|.15..|.17..|..19..|A005408 k=4.|..1..|..4..|..6..|..7..|..9..|.13..|.16..|.18..|.19..|..21..|new k=5.|..1..|..5..|..7..|..8..|..9..|.11..|.16..|.21..|.25..|..27..|A137469 k=6.|..1..|..6..|..8..|..9..|.10..|.11..|.13..|.19..|.25..|..31..|A138103 k=7.|..1..|..7..|..9..|.10..|.11..|.12..|.13..|.15..|.22..|..29..|new k=8.|..1..|..8..|.10..|.11..|.12..|.13..|.14..|.15..|.17..|..25..|new k=9.|..1..|..9..|.11..|.12..|.13..|.14..|.15..|.16..|.17..|..19..|new k=10|..1..|.10..|.12..|.13..|.14..|.15..|.16..|.17..|.18..|..19..|new ===================================================================
Programs
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Maple
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
Formula
A(k,n) = n-th number with an odd number of 1's in base k expansion.
Extensions
Corrected and extended by R. J. Mathar, May 17 2008
Comments