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

0,3

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

Table of n, a(n) for n=0..30.

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000930, A048715, A350311, A350312.

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

Sequence in context: A355892 A055992 A115814 * A171758 A115798 A077439

Adjacent sequences: A350212 A350213 A350214 * A350216 A350217 A350218

Keyword

nonn,base

Author

A.H.M. Smeets, Dec 19 2021

Status

approved