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A138607
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List first A008578(1-1) odd numbers, then first A008578(2-1) even numbers, then the next A008578(3-1) odd numbers, then the next A008578(4-1) even numbers, etc.
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3
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1, 2, 4, 3, 5, 7, 6, 8, 10, 12, 14, 9, 11, 13, 15, 17, 19, 21, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The original name was "PrimCon 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
| Index entries for sequences that are permutations of the natural numbers
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FORMULA
| If n < 3, a(n) = n. If n-2 = A007504(A083375(n-2)), then a(n) = a(n-1-A000040(A083375(n-2)))+2, otherwise a(n) = a(n-1)+2. - Antti Karttunen, Oct 05 2009.
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EXAMPLE
| 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,...
The sequence is formed by concatenating subsequences S1, S2, S3, ..., each of finite length. The subsequence S1 consists of the element 1, after which the n-th subsequence has p(n-1) elements, where p(n) denotes n-th prime number, A000040(n). Each subsequence is nondecreasing and the difference between two consecutive elements in the same subsequence is 2.
thus we have
S1={1}
S2={2,4}
S3={3,5,7}
S4={6,8,10,12,14}
S5={9,11,13,15,17,19,21}
S6={16,18,20,22,24,26,28,30,32,34,36}
...
and concatenating them S1/S2/S3/S4/S5/S6/... gives this sequence.
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PROG
| (MIT Scheme:) (define (A138607 n) (if (< n 3) n (let ((k (A083375 (- n 2)))) (if (= (- n 2) (A007504 k)) (+ 2 (A138607 (- n 1 (A000040 k)))) (+ 2 (A138607 (-1+ n)))))))
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CROSSREFS
| Inverse: A166014. Cf. A138606-A138609, A138612.
Sequence in context: A074146 A143097 A074147 * A166014 A199779 A093506
Adjacent sequences: A138604 A138605 A138606 * A138608 A138609 A138610
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KEYWORD
| nonn
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AUTHOR
| Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), May 14 2008
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EXTENSIONS
| 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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