A173025 Numbers whose binary representation contains no isolated digits "11".

0, 1, 2, 4, 5, 7, 8, 9, 10, 14, 15, 16, 17, 18, 20, 21, 23, 28, 29, 30, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 46, 47, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 71, 72, 73, 74, 78, 79, 80, 81, 82, 84, 85, 87, 92, 93, 94, 95, 112, 113, 114, 116, 117, 119, 120, 121, 122

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Formula

A173021(a(n+1)) = A173021(a(n)) + 1.

Mathematica

Select[Range[0, 150], FreeQ[Split[IntegerDigits[#, 2]], {1, 1}] &] (* Paolo Xausa, Oct 15 2024 *)

Prog

(Python)
from math import comb
from sympy import fibonacci
from oeis_sequences.OEISsequences import bisection
def A173025(n):
    def f(x):
        s = bin(x)[-1:1:-1]
        t = '0'+s+'0'
        return n+x-sum(sum(fibonacci(k+1)*comb(i-k+1, k) for k in range(i+1))  for i in range(len(s)) if s[i]=='1' and not '0110' in '0'+t[i+2:])-('0110' not in t)
    return bisection(f, n-1, n-1) # Chai Wah Wu, Jun 10 2026

Crossrefs

Cf. A007088, A144795, A173021.

A173024 is a subsequence.

Sequence in context: A026367 A039069 A285423 * A203463 A391576 A223909

Adjacent sequences: A173022 A173023 A173024 * A173026 A173027 A173028

Keyword

base,nonn

Author

Reinhard Zumkeller, Feb 07 2010

Status

approved