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A136081
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Array, read by antidiagonals, numbers with an odd number of 1's in base k expansion.
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1
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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
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OFFSET
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1,3
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COMMENTS
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Infinite number of analogs (one per row) of odious numbers.
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LINKS
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FORMULA
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A(k,n) = n-th number with an odd number of 1's in base k expansion.
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EXAMPLE
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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
===================================================================
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MAPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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