A350215 A048715, written in binary.

0, 1, 10, 100, 1000, 1001, 10000, 10001, 10010, 100000, 100001, 100010, 100100, 1000000, 1000001, 1000010, 1000100, 1001000, 1001001, 10000000, 10000001, 10000010, 10000100, 10001000, 10001001, 10010000, 10010001, 10010010, 100000000, 100000001, 100000010

Offset: 0

Author

A.H.M. Smeets, Dec 19 2021

Keywords

• nonn
• base

Comments

Narayana weighted representation of n (the top version).

a(n) equals binary representation of m, if and only if A350311(m) = n and for all k > m A350311(k) > n.

Links

• A.H.M. Smeets, The design of greedy number representations

Crossrefs

Cf. A000930, A048715, A350311, A350312.

Fibonacci representations: A014417 (Zeckendorf), A104326 (dual Zeckendorf).

Programs

Mathematica

bin[n_] := FromDigits[IntegerDigits[n, 2]]; q[n_] := BitAnd[n, 6*n] == 0; bin /@ Select[Range[0, 250], q] (* Amiram Eldar, Jan 27 2022 *)

Python

def c(b): return not "11" in b and not "101" in b
def auptod(digits):
    return [int(b) for b in (bin(k)[2:] for k in range(2**digits)) if c(b)]
print(auptod(9)) # Michael S. Branicky, Dec 20 2021

Formula

Regular expression 0|(1000*)*10*.