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Search: id:A026272
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| A026272 |
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a(n) = a(m) if a(m) has already occurred exactly once and n = a(m) + m + 1, else a(n) = least positive integer that has not yet occurred. |
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+0
10
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| 1, 2, 1, 3, 2, 4, 5, 3, 6, 7, 4, 8, 5, 9, 10, 6, 11, 7, 12, 13, 8, 14, 15, 9, 16, 10, 17, 18, 11, 19, 20, 12, 21, 13, 22, 23, 14, 24, 15, 25, 26, 16, 27, 28, 17, 29, 18, 30, 31, 19, 32, 20, 33, 34, 21, 35, 36, 22, 37, 23, 38, 39, 24, 40, 41, 25
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence displays every positive integer exactly twice and the gap between the two occurrences of n contains exactly n other values. The first occurrence of n precedes the first occurrence of n+1. (cont.)
Also related to the Wythoff array (A035513) and the Para-Fibonacci sequence (A035513) where every positive integer is displayed exactly once in the whole array. Take any integer n in A026272 and let C = number of terms from the beginning of the sequence to the second occurrence of n. Then C = (2nd term after n in the applicable sequence for n in A035513). (cont.)
Also in the second occurrence of n in A026272, let N=n ( - one term) = (first term value after n in the applicable sequence for n in A035513). In this format the second occurrence of n in A026272 will produce in A035513, n itself and two of the succeeding terms of n in the Wythoff array where every positive integer can only be displayed once. (cont.)
In A026272 if |a(n)-a(n+1)| > 10 then phi ~ a(n)/|a(n)-a(n+1)|. When n -> infinity it will converge to phi. - Dan Joyce (danj_536(AT)msn.com), Apr 13 2001
Or, put a copy of n in A000027 n places further along! - Zak Seidov (zakseidov(AT)yahoo.com), May 24 2008
Another version would prefix this sequence with two leading 0's (see the Angelini reference). If we use this form and write down the indices of the two 0's, the two 1's, the two 2's, the two 3's, etc., then we get A072061. - Jacques ALARDET (jacques.alardet(AT)free.fr), Jul 26 2008
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REFERENCES
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E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, Volume 59 (Jeux math'), April/June 2008, Paris.
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LINKS
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Zak Seidov, Table of n, a(n) for n = 1..1000.
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MATHEMATICA
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s=Range[1000]; n=0; Do[n++; s=Insert[s, n, Position[s, n][[1]]+n+1], {500}]; A026272=Take[s, 1000] - Zak Seidov (zakseidov(AT)yahoo.com), May 24 2008
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CROSSREFS
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a(n) = A026242(n+2) - 1 = A026350(n+3) - 2 = A026354(n+4) - 3.
Cf. A000027, A035513.
Sequence in context: A034391 A144241 A094173 this_sequence A022447 A117194 A024467
Adjacent sequences: A026269 A026270 A026271 this_sequence A026273 A026274 A026275
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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