A290155 Let a(n) be the sequence of 0's and 1's that represents n. Then a(0) = 0; and a((1b)_2) = 1a(|b|)b where |b| denotes the length of b.

0, 10, 1100, 1101, 1110000, 1110001, 1110010, 1110011, 11101000, 11101001, 11101010, 11101011, 11101100, 11101101, 11101110, 11101111, 111100000000, 111100000001, 111100000010, 111100000011, 111100000100, 111100000101, 111100000110, 111100000111

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Donald E. Knuth, Selected Papers on Fun and Games, Stanford, California: Center for the Study of Language and Information (2011).

Example

(1)_2 = 1,    so a(1) = 1a(0)    = 10.
(2)_2 = 10,   so a(2) = 1a(1)0   = 1100.
(3)_2 = 11,   so a(3) = 1a(1)1   = 1101.
(4)_2 = 100,  so a(4) = 1a(2)00  = 1110000.
(5)_2 = 101,  so a(5) = 1a(2)01  = 1110001.
(6)_2 = 110,  so a(6) = 1a(2)10  = 1110010.
(7)_2 = 111,  so a(7) = 1a(2)11  = 1110011.
(8)_2 = 1000, so a(8) = 1a(3)000 = 11101000.

Prog

(Python)
def a(n):
    b = bin(n)[3:]
    return 0 if n == 0 else int('1' + str(a(len(b))) + b)
print([a(n) for n in range(51)]) # Indranil Ghosh, Jul 22 2017

Crossrefs

Cf. A007088 (binary numbers).

Sequence in context: A268229 A307723 A071672 * A265849 A122230 A138147

Adjacent sequences: A290152 A290153 A290154 * A290156 A290157 A290158

Keyword

nonn

Author

Seiichi Manyama, Jul 22 2017

Status

approved