login
A336533
Lexicographically earliest sequence of positive terms such that for any n > 0, n = Sum_{k >= 0} b(k)*a(k+1) where Sum_{k >= 0} b(k)*2^k is the binary expansion of a(n).
1
1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 23, 26, 27, 29, 30, 31, 47, 55, 58, 59, 61, 62, 63, 93, 94, 95, 111, 119, 122, 123, 125, 126, 127, 191, 221, 222, 223, 239, 247, 250, 251, 253, 254, 255, 382, 383, 447, 477, 478, 479, 495, 503, 506, 507, 509, 510, 511, 767
OFFSET
1,2
COMMENTS
In other words, the binary expansion of the n-th term encodes a partition of n into distinct terms of the sequence.
This sequence is complete (as any integer can be written as a sum of distinct terms of this sequence).
FORMULA
a(Sum_{k = 1..n} a(k)) = 2^n - 1 for any n > 0.
EXAMPLE
The first terms, alongside their binary representation and the corresponding partition of n, are:
n a(n) bin(a(n)) Partition of n
-- ---- --------- -------------------------
1 1 1 a(1)
2 2 10 a(2)
3 3 11 a(2) + a(1)
4 5 101 a(3) + a(1)
5 6 110 a(3) + a(2)
6 7 111 a(3) + a(2) + a(1)
7 10 1010 a(4) + a(2)
8 11 1011 a(4) + a(2) + a(1)
9 13 1101 a(4) + a(3) + a(1)
10 14 1110 a(4) + a(3) + a(2)
11 15 1111 a(4) + a(3) + a(2) + a(1)
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A293430 A087006 A345297 * A359782 A235991 A327906
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 26 2020
STATUS
approved