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Search: id:A138606
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| A138606 |
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List first F(1) odd numbers, then first F(2) even numbers (starting from 2), then the next F(3) odd numbers, then the next F(4) even numbers, etc, where F(n) = A000045(n), the nth Fibonacci number. |
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+0
7
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| 1, 2, 3, 5, 4, 6, 8, 7, 9, 11, 13, 15, 10, 12, 14, 16, 18, 20, 22, 24, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77
(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 "FibCon sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614), which are all monotone, while this sequence is a bijection of natural numbers.
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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FORMULA
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a(n) = A166012(A072649(n)-1) + 2*(n-A000045(1+A072649(n))). - Antti Karttunen, Oct 05 2009.
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EXAMPLE
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Let us separate natural numbers into odd (A005408) and even numbers (A005843):
1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,...
2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,...
then we get the following subsequences:
S1={1}
S2={2}
S3={3,5}
S4={4,6,8}
S5={7,9,11,13,15}
S6={10,12,14,16,18,20,22,24}
...
and concatenating them S1/S2/S3/S4/S5/... gives this sequence.
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PROGRAM
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(MIT Scheme:) (define (A138606 n) (if (zero? n) n (+ (A166012 (-1+ (A072649 n))) (* 2 (- n (A000045 (1+ (A072649 n))))))))
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CROSSREFS
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Inverse: A166013. A000035(a(n)) = A000035(A072649(n)). Cf. A138607-A138609, A138612.
Sequence in context: A081241 A075168 A075169 this_sequence A166013 A089864 A073290
Adjacent sequences: A138603 A138604 A138605 this_sequence A138607 A138608 A138609
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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 and Scheme-code added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Oct 05 2009
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