OFFSET
0,3
COMMENTS
The definition is recursive: a(n) depends on prior terms (a(0), ..., a(n-1)); a(0) = 0 corresponds to an empty sum.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..10000
FORMULA
a(2^k) = 2^k.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k's
-- ---- -------------------------
0 0 {}
1 1 {0}
2 2 {0, 1}
3 1 {0}
4 4 {0, 1, 2, 3}
5 2 {0, 2}
6 3 {0, 1, 3}
7 1 {0}
8 8 {0, 1, 2, 3, 4, 5, 6, 7}
9 4 {0, 2, 4, 5}
10 6 {0, 1, 3, 4, 7, 9}
11 3 {0, 4, 9}
12 8 {0, 1, 2, 3, 5, 6, 7, 11}
MAPLE
a:= proc(n) option remember; add(
`if`(Bits[And](n, a(j))=0, 1, 0), j=0..n-1)
end:
seq(a(n), n=0..80); # Alois P. Heinz, Feb 28 2022
PROG
(PARI) for (n=1, #a=vector(75), print1 (a[n]=sum(k=1, n-1, bitand(a[k], n-1)==0)", "))
(Python)
a = []
[a.append(sum(a[k] & n == 0 for k in range(n))) for n in range(74)]
print(a) # Michael S. Branicky, Feb 24 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Feb 23 2022
STATUS
approved