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A252055
Number of products A000201(i)*A001950(j) = n.
1
0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 0, 3, 0, 2, 1, 1, 0, 2, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 0, 3, 1, 1, 1, 1, 0, 6, 0, 1, 1, 1, 1, 1, 0, 1, 1, 3, 0, 1, 1, 1, 1, 1, 1, 3, 0, 4, 1, 0, 1, 3, 1, 2
OFFSET
1,15
COMMENTS
A000201 and A001950 are the lower and upper Wythoff sequences, which partition the nonnegative integers.
Does this sequence include every nonnegative integer? What is the maximal number of consecutive 0's? What is the maximal number of consecutive 1's?
LINKS
EXAMPLE
a(312) counts these 7 products: 3*104, 4*78, 6*52, 8*39, 12*26, 24*13, 156*2
MAPLE
N:= 1000: # to get a(1) to a(N)
A201:= [seq(floor(n*phi), n=1..N)]:
A1950:= [seq(floor(n*phi^2), n=1..N)]:
A:= Vector(N):
for i from 1 to N do
for j from 1 do
m:= A201[i]*A1950[j];
if m > N then break fi;
A[m]:= A[m]+1;
od
od:
convert(A, list); # Robert Israel, Dec 23 2014
MATHEMATICA
r = (1 + Sqrt[5])/2; s = r/(r - 1); t = Flatten[Table[Floor[r*j]*Floor[s*k], {j, 1, 300}, {k, 1, 300}]]; a[n_] := Count[t, n]; u = Table[a[n], {n, 1, 300}]
CROSSREFS
Sequence in context: A140397 A120614 A287516 * A324144 A320836 A375512
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Dec 23 2014
STATUS
approved