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).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Binary plot of the first 1000 terms
Rémy Sigrist, PARI program for A336533
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Sep 26 2020
STATUS
approved