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A286905
Positions of 1 in A286903; complement of A286904.
3
1, 2, 5, 6, 9, 10, 11, 14, 15, 18, 19, 20, 23, 24, 27, 28, 31, 32, 33, 36, 37, 40, 41, 42, 45, 46, 49, 50, 53, 54, 55, 58, 59, 62, 63, 64, 67, 68, 71, 72, 73, 76, 77, 80, 81, 84, 85, 86, 89, 90, 93, 94, 95, 98, 99, 102, 103, 106, 107, 108, 111, 112, 115, 116
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(n) - a(n-1) is in {1,3} for n>=2, and a(n)/n -> -1 + 2*sqrt(2).
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
From Ridouane Oudra, Nov 21 2024: (Start)
a(n) = 2*floor(n*sqrt(2)) - n.
a(n) = 2*A001951(n) - n.
a(n) = A286909(n) - n. (End)
EXAMPLE
As a word, A286804 = 11001100111001100111001..., in which 1 is in positions 1,2,5,6,9,...
MAPLE
seq(2*floor(n*sqrt(2))-n, n=1..60); # Ridouane Oudra, Nov 21 2024
MATHEMATICA
s = Nest[Flatten[# /. {0 -> 1, 1 -> {1, 1, 0}}] &, {1}, 7] (* A080764 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"0" -> "00"}]
st = ToCharacterCode[w1] - 48 ; (* A286903 *)
Flatten[Position[st, 0]]; (* A286904 *)
Flatten[Position[st, 1]]; (* A286905 *)
CROSSREFS
Cf. A080764, A286903, A286904, A001951, A286909.
Sequence in context: A284492 A224779 A171888 * A028946 A213713 A031461
Adjacent sequences: A286902 A286903 A286904 * A286906 A286907 A286908
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 17 2017
STATUS
approved

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Last modified February 26 21:14 EST 2025. Contains 381238 sequences.
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