

A043570


Numbers whose base2 representation has exactly 3 runs.


3



5, 9, 11, 13, 17, 19, 23, 25, 27, 29, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 65, 67, 71, 79, 95, 97, 99, 103, 111, 113, 115, 119, 121, 123, 125, 129, 131, 135, 143, 159, 191, 193, 195, 199, 207, 223, 225, 227, 231, 239, 241, 243, 247
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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 base2 representation of a number of the form 2^k+1 > 3 consists of a single 1, followed by a block of k1 0's, followed by a last single 1. Also, A000215 \ {3} is another subsequence, since the base2 representation of a Fermat number 2^(2^k)+1 > 3 consists of a single 1, followed by a block of 2^k1 0's, followed by a last single 1.  Bernard Schott, Mar 09 2023


LINKS



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^n2^m+2^k1, k=1..m1), m=n1..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(k1, 1, 1) for i in range(1, j))


CROSSREFS

Cf. A082554 (subsequence of primes).


KEYWORD

nonn,base


AUTHOR



STATUS

approved



