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Search: id:A138608
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| A138608 |
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List first F(1) numbers from A016777, then first F(2) numbers from A016789, then the first F(3) numbers from A008585 (starting from 3), then the next F(4) numbers from A016777, then the next F(5) numbers from A016789, then the next F(6) numbers from A008585, etc, where F(n) = A000045(n), the nth Fibonacci number. |
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+0
3
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| 1, 2, 3, 6, 4, 7, 10, 5, 8, 11, 14, 17, 9, 12, 15, 18, 21, 24, 27, 30, 13, 16, 19, 22, 25, 28, 31, 34, 37, 40, 43, 46, 49, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The original name was "Generalized FibCon sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614 and the paper by Iannucci & Mills-Taylor), which are all monotone, while this sequence is a bijection of natural numbers.
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LINKS
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Douglas E. Iannucci, Donna Mills-Taylor, On Generalizing the Connell Sequence, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7
Index entries for sequences that are permutations of the natural numbers
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FORMULA
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If n < 4, a(n) = n. If n = A000045(A072649(n)+1), then a(n) = a(n-1-A000045(A072649(n)))+3, otherwise a(n) = a(n-1)+3. - Antti Karttunen, Oct 05 2009.
1. The sequence is formed by concatenating subsequences S0,S1, S2, ..., each of finite length. 2. The subsequence S0 consists of the element 1. 3. The n-th subsequence has F(n) elements, F(n) denotes n-th Fibonacci number. 4. Each subsequence is nondecreasing and the difference between two consecutive elements in the same subsequence is 3.
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EXAMPLE
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Let us separate natural numbers into three disjoint sets (A016777, A016789 and A008585):
1,4,7,10,13,16,19,22,25,28,31,...
2,5,8,11,14,17,20,23,26,29,32,...
3,6,9,12,15,18,21,24,27,30,33,...
then
S0={1}
S1={2}
S2={3,6}
S3={4,7,10}
S4={5,8,11,14,17}
S5={9,12,15,18,21,24,27,30}
...
and concatenating S0/S1/S2/S3/S4/S5/... gives this sequence.
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PROGRAM
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(MIT Scheme:) (define (A138608 n) (if (< n 4) n (let ((k (A072649 n))) (if (= n (A000045 (1+ k))) (+ 3 (A138608 (- n 1 (A000045 k)))) (+ 3 (A138608 (-1+ n)))))))
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CROSSREFS
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Inverse: A166015. A010872(a(n)) = A010872(A072649(n)). Cf. A138606-A138609, A138612.
Sequence in context: A156688 A019567 A098286 this_sequence A092283 A099900 A138728
Adjacent sequences: A138605 A138606 A138607 this_sequence A138609 A138610 A138611
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KEYWORD
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easy,nonn
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AUTHOR
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Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), May 14 2008
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EXTENSIONS
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Edited, extended, starting offset changed from 0 to 1, and Scheme-code added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 05 2009
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