OFFSET
1,1
COMMENTS
Numbers of the form 2^n - 2^m + 2^k - 1 for n > m > k > 0. - Robert Israel, Jan 11 2018
A000051 \ {2, 3} is a subsequence, since the base-2 representation of a number of the form 2^k+1 > 3 consists of a single 1, followed by a block of k-1 0's, followed by a last single 1. Also, A000215 \ {3} is another subsequence, since the base-2 representation of a Fermat number 2^(2^k)+1 > 3 consists of a single 1, followed by a block of 2^k-1 0's, followed by a last single 1. - Bernard Schott, Mar 09 2023
Numbers k such that A005811(k) = 3. - Michel Marcus, Mar 10 2023
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
115 = 1110011_2, which is a block of three 1's, followed by a block of two 0's, followed by a block of two 1's, so 115 is a term.
MAPLE
seq(seq(seq(2^n-2^m+2^k-1, k=1..m-1), m=n-1..2, -1), n=2..10); # Robert Israel, Jan 11 2018
PROG
(Python)
from itertools import count, islice
def agen(): yield from ((1<<k)-(1<<j)+(1<<i)-1 for k in count(1) for j in range(k-1, 1, -1) for i in range(1, j))
print(list(islice(agen(), 53))) # Michael S. Branicky, Feb 25 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
STATUS
approved