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Search: id:A118462
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| A118462 |
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Decimal equivalent of binary encoding of partitions into distinct parts. |
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+0
2
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| 0, 1, 2, 3, 4, 5, 8, 6, 9, 16, 7, 10, 17, 32, 11, 12, 18, 33, 64, 13, 19, 20, 34, 65, 128, 14, 21, 24, 35, 36, 66, 129, 256, 15, 22, 25, 37, 40, 67, 68, 130, 257, 512, 23, 26, 38, 41, 48, 69, 72, 131, 132, 258, 513, 1024, 27, 28, 39, 42, 49, 70, 73, 80, 133, 136, 259, 260, 514
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A part of size k in the partition makes the 2^(k-1) bit of the number be 1. The partitions of n are in reverse Mathematica ordering, so that each row is in ascending order. This is a permutation of the nonnegative integers.
The sequence is the concatenation of the sets: e_n={j>=0: A029931(j)=n}, n=0,1,...: e_0={0}, e_1={1}, e_2={2}, e_3={3,4}, e_4={5,8}, e_5={6,9,16}, e_6={7,10,17,32}, e_7={11,12,18.33.64}, ... . [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 16 2009]
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LINKS
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Index entries for sequences that are permutations of the natural numbers
V. Shevelev, A recursion for divisor function over divisors belonging to a prescribed finite sequence of positive integers and a solution of the Lahiri problem for divisor function sigma_x(n) [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), Mar 17 2009]
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EXAMPLE
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Partition 11 is [4,2], which gives binary 1010 (2^(4-1)+2^(2-1)), or 10, so a(11)=10.
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CROSSREFS
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Cf. A118463, A118457, A000009 (row lengths).
Cf. A089633 (first column), A000079 (last in each column). [From Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Mar 16 2009]
Sequence in context: A162371 A146941 A085176 this_sequence A122317 A130992 A122318
Adjacent sequences: A118459 A118460 A118461 this_sequence A118463 A118464 A118465
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KEYWORD
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base,nonn,tabf
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AUTHOR
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Frank Adams-Watters (FrankTAW(AT)Netscape.net), Apr 28 2006
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