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Search: id:A146085
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| A146085 |
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Positive integers a(n) such that for every integer m==1 (mod 3), m>=4, there exists a unique representation of m as a sum of the form a(l)+3a(s) |
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+0
3
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| 1, 4, 7, 28, 31, 34, 55, 58, 61, 244, 247, 250, 271, 274, 277, 298, 301, 304, 487, 490, 493, 514, 517, 520, 541, 544, 547
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Theorem. An integer is in the sequence iff in its expansion on base 3 all digits at the k-th position from the end, k=3, 5, 7, ..., are zeros while the first digit from the end is 1. To get the decomposition of m==1(mod 3) as sum a(l)+3a(s), write m-3 as Sum b_j 3^j, then a(l) = 1 + Sum_{j odd} b_j 3^j.
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EXAMPLE
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If m=46, then we have 46=1*3^0+2*3^2+1*3^3, thus a(l)=1+1*3^3=28 and and the required decomposition is: 46=28+3*4, such that a(s)=4. We see that l=4, s=2, i.e. "index coordinates" of 46 are (4, 2). Thus we have a one-to-one map of integers m==1(mod 3), m>=4, to the positive lattice points on the plane.
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CROSSREFS
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Cf. A145812 A145818
Sequence in context: A075686 A077441 A076148 this_sequence A061668 A128386 A149074
Adjacent sequences: A146082 A146083 A146084 this_sequence A146086 A146087 A146088
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KEYWORD
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nonn
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AUTHOR
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Vladimir Shevelev (shevelev(AT)bgu.ac.il), Oct 27 2008
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