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 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
 0, 10, 1100, 1101, 1110000, 1110001, 1110010, 1110011, 11101000, 11101001, 11101010, 11101011, 11101100, 11101101, 11101110, 11101111, 111100000000, 111100000001, 111100000010, 111100000011, 111100000100, 111100000101, 111100000110, 111100000111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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

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Last modified April 18 10:56 EDT 2021. Contains 343087 sequences. (Running on oeis4.)