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A191340
(A022839 mod 2)+(A108598 mod 2)
4
1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 1
OFFSET
1,5
COMMENTS
Let r=sqrt(5) and s=r/(r-1). There numbers yield the following two complementary Beatty sequences:
A022839(n)=[nr], A108598(n)=[ns], where [ ]=floor.
A191340(n)=the number of odd numbers in {[nr], [ns]}.
LINKS
FORMULA
a(n)=([nr] mod 2)+([ns] mod 2), where r=sqrt(5), s=r/(r-1), [ ]=floor.
MATHEMATICA
r = Sqrt[5]; s = r/(r - 1); h = 120;
u = Table[Floor[n*r], {n, 1, h}] (* A022839 *)
v = Table[Floor[n*s], {n, 1, h}] (* A108598 *)
w = Mod[u, 2] + Mod[v, 2] (* A191340 *)
Flatten[Position[w, 0]] (* A191380 *)
Flatten[Position[w, 1]] (* A191381 *)
Flatten[Position[w, 2]] (* A191382 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 01 2011
STATUS
approved