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A080754
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a(n) = ceiling(n*(1+sqrt(2))).
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5
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3, 5, 8, 10, 13, 15, 17, 20, 22, 25, 27, 29, 32, 34, 37, 39, 42, 44, 46, 49, 51, 54, 56, 58, 61, 63, 66, 68, 71, 73, 75, 78, 80, 83, 85, 87, 90, 92, 95, 97, 99, 102, 104, 107, 109, 112, 114, 116, 119, 121, 124, 126, 128, 131, 133, 136, 138, 141, 143, 145
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Integer solutions >0 to the equation x=ceiling(r*floor(x/r)), where r=1+sqrt(2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 14 2004
Equivalently, numbers m such that {rm} <= {r}, where r=2^(1/2) and { } denotes fractional part.
Andrew Plewe, May 18 2007, observed that the sequence defined by a(n) = ceiling(n*(1+sqrt(2))) appeared to give the same numbers as the sequence, originally due to Clark Kimberling (ck6(AT)evansville.edu), Jul 01 2006, defined by: numbers m such that {rm} <= {r}, where r=2^(1/2). That these sequences are indeed the same was shown by David Applegate. This follows since the complements of the two sequences are the same, which is shown in the comments on A080755.
It appears that A080754 gives the positions of 1 in the zero-one sequence A188037; [From Clark Kimberling, Mar 19 2011]
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LINKS
| 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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FORMULA
| a(1) = 3; for n>1, a(n) = a(n-1) + 3 if n is in sequence, a(n) = a(n-1) + 2 if not.
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CROSSREFS
| Equals A003151 + 1. This and its complement A080755 partition the integers >= 2.
Sequence in context: A195170 A079527 A033033 * A198083 A195168 A047218
Adjacent sequences: A080751 A080752 A080753 * A080755 A080756 A080757
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre and N. J. A. Sloane (njas(AT)research.att.com), Mar 09 2003
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 08 2007
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