A247647 Binary numbers that begin and end with 1 and do not contain two adjacent zeros.

1, 11, 101, 111, 1011, 1101, 1111, 10101, 10111, 11011, 11101, 11111, 101011, 101101, 101111, 110101, 110111, 111011, 111101, 111111, 1010101, 1010111, 1011011, 1011101, 1011111, 1101011, 1101101, 1101111, 1110101, 1110111, 1111011, 1111101, 1111111, 10101011, 10101101, 10101111, 10110101, 10110111, 10111011, 10111101

Offset: 1

Author

N. J. A. Sloane, Sep 25 2014

Keywords

• nonn
• base

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1000

Crossrefs

See A247648 for the decimal equivalents.

Cf. A007088, A247649, A253085.

Programs

Haskell

a247647 = a007088 . a247648  -- Reinhard Zumkeller, Sep 25 2014

Mathematica

With[{upto=500},Map[FromDigits,Select[IntegerString[Range[1,upto,2],2],StringFreeQ[#,"00"]&]]] (* Paolo Xausa, Dec 06 2023 *)

Python

A247647_list = [int(bin(n)[2:]) for n in range(1,10**5) if n % 2 and not '00' in bin(n)]
# Chai Wah Wu, Sep 25 2014

Formula

a(n) = A007088(A247648(n)).