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Search: id:A004956
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| A004956 |
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Ceiling of n*phi, phi = (1+sqrt(5))/2. |
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+0
5
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| 0, 2, 4, 5, 7, 9, 10, 12, 13, 15, 17, 18, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 38, 39, 41, 43, 44, 46, 47, 49, 51, 52, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 75, 77, 78, 80, 81, 83, 85, 86, 88, 89
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(0)=0, a(1)=2; for n>1, a(n)=a(n-1)+2 if n is already in the sequence, a(n)=a(n-1)+1 otherwise.
Integer solutions to the equation x=ceiling(phi*floor(x/phi)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004
Benoit Cloitre, Mar 05 2007: (Start) The following is an alternative way to obtain this sequence. NP means "term not in parentheses". Write down the natural numbers and mark the least NP, which is 1:
1* 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
Take the 1st NP (which is 1) and parenthesize it; mark the least NP (which is 2):
(1*) 2* 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
Take the 2nd NP (which is 3) and parenthesize it; mark the next NP (which is 4):
(1*) 2* (3) 4* 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
Take the 4th NP (which is 6) and parenthesize it; mark the next NP (which is 5):
(1*) 2* (3) 4* 5* (6) 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
Continuing in this way we obtain
(1*) 2* (3) 4* 5* (6) 7* (8) 9* 10* (11) 12* 13* (14) 15* (16) 17* (18) 19* ...
The starred entries (after the first) give the sequence. (End)
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LINKS
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B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
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CROSSREFS
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Essentially same as A026351.
Sequence in context: A026463 A087063 A047497 this_sequence A026351 A047212 A121347
Adjacent sequences: A004953 A004954 A004955 this_sequence A004957 A004958 A004959
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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