This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A350215 #58 Feb 18 2022 21:01:19 %S A350215 0,1,10,100,1000,1001,10000,10001,10010,100000,100001,100010,100100, %T A350215 1000000,1000001,1000010,1000100,1001000,1001001,10000000,10000001, %U A350215 10000010,10000100,10001000,10001001,10010000,10010001,10010010,100000000,100000001,100000010 %N A350215 A048715, written in binary. %C A350215 Narayana weighted representation of n (the top version). %C A350215 a(n) equals binary representation of m, if and only if A350311(m) = n and for all k > m A350311(k) > n. %H A350215 A.H.M. Smeets, <a href="/A350215/a350215.pdf">The design of greedy number representations</a> %F A350215 Regular expression 0|(1000*)*10*. %t A350215 bin[n_] := FromDigits[IntegerDigits[n, 2]]; q[n_] := BitAnd[n, 6*n] == 0; bin /@ Select[Range[0, 250], q] (* _Amiram Eldar_, Jan 27 2022 *) %o A350215 (Python) %o A350215 def c(b): return not "11" in b and not "101" in b %o A350215 def auptod(digits): %o A350215 return [int(b) for b in (bin(k)[2:] for k in range(2**digits)) if c(b)] %o A350215 print(auptod(9)) # _Michael S. Branicky_, Dec 20 2021 %Y A350215 Cf. A000930, A048715, A350311, A350312. %Y A350215 Fibonacci representations: A014417 (Zeckendorf), A104326 (dual Zeckendorf). %K A350215 nonn,base %O A350215 0,3 %A A350215 _A.H.M. Smeets_, Dec 19 2021