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2, 3, 5, 7, 9, 10, 12, 14, 15, 17, 19, 20, 22, 24, 26, 27, 29, 31, 32, 34, 36, 38, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 73, 75, 77, 79, 80, 82, 84, 85, 87, 89, 90, 92, 94, 96, 97, 99, 101, 102, 104, 106, 108, 109, 111, 113, 114, 116, 118
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OFFSET
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1,1
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COMMENTS
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The old entry with this sequence number was a duplicate of A003687.
The answer to Kimberling's question is: yes. See the Bosma-Dekking-Steiner paper. - Michel Dekking, Oct 14 2018
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LINKS
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FORMULA
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[a(n)*r] = n + [n*r] for n >= 1, where r = sqrt(2) and [ ] = floor.
{a(n)*sqrt(2)} > 1/2 if n is in A120753, where { } = fractional part; otherwise n is in A120752. (End)
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MATHEMATICA
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t = Nest[Flatten[# /. {0->{0, 1, 1}, 1->{0, 1}}] &, {0}, 5] (*A189687*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A086377 conjectured *)
Flatten[Position[t, 1]] (* A081477 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189688*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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