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A284625
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Positions of 2 in A284749.
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4
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3, 6, 7, 10, 13, 14, 17, 18, 21, 24, 25, 28, 31, 32, 35, 36, 39, 42, 43, 46, 47, 50, 53, 54, 57, 60, 61, 64, 65, 68, 71, 72, 75, 78, 79, 82, 83, 86, 89, 90, 93, 94, 97, 100, 101, 104, 107, 108, 111, 112, 115, 118, 119, 122, 123, 126, 129, 130, 133, 136, 137
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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This sequence and A214971 and A284624 partition the positive integers into sequences with slopes t = (5+sqrt(5))/2, u = (5+sqrt(5))/2, v = sqrt(5), where 1/t + 1/u + 1/v = 1. The positions of 0 in A284749 are given by A214971, and of 1, by A284624.
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LINKS
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FORMULA
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a(n) = 2*floor(n*phi) - n + 2 (Example 30 in Allouche and Dekking). - Michel Dekking, Oct 08 2018
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EXAMPLE
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As a word, A284749 = 012012201201220122..., in which 2 is in positions 3,6,7,10,...
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {0, 1}, 1 -> {0}}] &, {0}, 13] (* A003849 *)
w = StringJoin[Map[ToString, s]]
w1 = StringReplace[w, {"001" -> "2"}]
st = ToCharacterCode[w1] - 48 (* A284749 *)
Flatten[Position[st, 0]] (* A214971 *)
Flatten[Position[st, 1]] (* A284624 *)
Flatten[Position[st, 2]] (* A284625 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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