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 A341766 a(n) = difference between the starting positions of the first digit of the binary representation of n, where n starts at its natural position in the string, and the second occurrence of the same string in the binary Champernowne string (starting at 0) 011011100101110111100010011010... (cf. A030190). 10
 3, 1, 4, 1, 12, 4, 5, 1, 32, 13, 2, 9, 15, 5, 6, 1, 80, 36, 12, 31, 76, 8, 23, 21, 39, 16, 69, 11, 18, 6, 7, 1, 192, 91, 38, 85, 3, 45, 20, 73, 163, 67, 2, 22, 40, 3, 45, 49, 95, 43, 139, 37, 118, 31, 3, 25, 46, 19, 137, 13, 21, 7, 8, 1, 448, 218, 100, 211, 31, 136, 79, 197, 429, 25, 58, 123 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Consider the infinite string 011011100101110111100010011010... (cf. A030190) formed by the concatenation of all binary digits of all nonnegative numbers. From the position of the first digit of the binary representation of n, where n starts as its natural position in the string, find the number of digits one has to move forward to get to the start of the second occurrence of n. This is a(n). LINKS Michael S. Branicky, Table of n, a(n) for n = 0..16383 Scott R. Shannon, Image of the first 100000 terms. FORMULA From Michael S. Branicky, Sep 16 2022: (Start) a(2^k-1) = 1, for k >= 1; a(2^k) = (k+1)*2^k, for k >= 0. (End) EXAMPLE a(0) = 3 as '0' starts at position 1 and appears again at position 4. a(1) = 1 as '1' starts at position 2 and appears again at position 3. a(4) = 12 as '100' starts at position 7 and appears again at position 19. a(7) = 1 as '111' starts at position 16 and appears again at position 17. a(8) = 32 as '1000' starts at position 19 and appears again at position 51. PROG (Python) def a(n): b = s = bin(n)[2:] while s.find(b, 1) < 0: n += 1; s += bin(n)[2:] return s.find(b, 1) print([a(n) for n in range(76)]) # Michael S. Branicky, Sep 16 2022 CROSSREFS Cf. A030190, A337227 (base 10), A296354, A296349, A296355. Sequence in context: A014413 A262072 A321743 * A131632 A051348 A253828 Adjacent sequences: A341763 A341764 A341765 * A341767 A341768 A341769 KEYWORD nonn,base AUTHOR Scott R. Shannon, Feb 19 2021 STATUS approved

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Last modified October 4 23:18 EDT 2023. Contains 365888 sequences. (Running on oeis4.)