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Search: id:A137362
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| A137362 |
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Positions at which the truncated square root of triangular numbers is unique. |
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1
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| 4, 7, 8, 11, 14, 17, 18, 21, 24, 25, 28, 31, 34, 35, 38, 41, 42, 45, 48, 49, 52, 55, 58, 59, 62, 65, 66, 69, 72, 75, 76, 79, 82, 83, 86, 89, 92, 93
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For any term p of the sequence B(p)=1+B(p-1)=-1+B(p+1)
For any of others p, one of these equalities is wrong.
The difference between two successive isolated terms of the sequence is always 3 or 7 (a(4)-a(1)=11-4=7, a(5)-a(4)=14-11=3)
The difference between the first or second terms of two successive pairs of the sequence is always 7 or 10 (a(6)-a(3)=17-7=7=a(7)-a(3)=18-8=10, a(9-a(6)=24-17=a(10)-a(7)=25-18=7)
For any n, c(n+13)-c(n) is always equal to 31 or 33 c(14)-c(1)=35-4=31 c(16)-c(3)=41-8=33.
Consider the slowly rising step function A061288 of truncated square roots. It attains unique (non-repeated) values A061288(j)=2,4,5,7,9,11,12,... once, whereas all others (1,3,6,8,10,..) occur at least twice. The values j+1 of the associated indices j=3,6,7,10,13,16 are listed here. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 05 2008
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CROSSREFS
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Adjacent sequences: A137359 A137360 A137361 this_sequence A137363 A137364 A137365
Sequence in context: A128373 A080578 A047347 this_sequence A024621 A000606 A061932
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), Apr 26 2008, Jun 06 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 05 2008
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