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A350215
A048715, written in binary.
11
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.
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
Fibonacci representations: A014417 (Zeckendorf), A104326 (dual Zeckendorf).
Sequence in context: A355892 A055992 A115814 * A171758 A115798 A077439
KEYWORD
nonn,base
AUTHOR
A.H.M. Smeets, Dec 19 2021
STATUS
approved