The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A300654 a(n) is the greatest k such that, for i = 1..k, the binary representation of i appears as a substring in the binary representation of 1/n (ignoring the radix point and adding trailing zeros if necessary in case of a terminating expansion). 2
 2, 2, 2, 2, 4, 2, 2, 2, 4, 4, 8, 2, 9, 2, 2, 2, 4, 4, 16, 4, 4, 8, 6, 2, 8, 9, 11, 2, 20, 2, 2, 2, 4, 4, 8, 4, 32, 16, 6, 4, 4, 4, 8, 8, 6, 6, 12, 2, 12, 8, 2, 9, 33, 11, 10, 2, 8, 20, 37, 2, 41, 2, 2, 2, 4, 4, 64, 4, 14, 8, 14, 4, 4, 32, 11, 16, 17, 6, 22, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, a(n) is the greatest k such that A300653(n, k) = k. This sequence has similarities with A144016: here we consider the binary expansion of 1/n, there the binary expansion of n. LINKS Rémy Sigrist, PARI program for A300654 FORMULA a(2*n) = a(n). a(n) = 2 iff n belongs to A300630. EXAMPLE For n = 19: - the binary expansion of 1/19 is 0.0000(110101111001010000) (with repeating digits in parentheses), - the first occurrence of the binary representation of k for k = 1..16 is:   k   bin(k)  bin(1/19) with bin(k) in parentheses   --  ------  ------------------------------------    1      1   0.0000(1)101...    2     10   0.00001(10)101...    3     11   0.0000(11)010...    4    100   0.000011010111(100)101...    5    101   0.00001(101)011...    6    110   0.0000(110)101...    7    111   0.000011010(111)100...    8   1000   0.00001101011110010(1000)011...    9   1001   0.000011010111(1001)010...   10   1010   0.00001(1010)111...   11   1011   0.0000110(1011)110...   12   1100   0.00001101011(1100)101...   13   1101   0.0000(1101)011...   14   1110   0.0000110101(1110)010...   15   1111   0.000011010(1111)001...   16  10000   0.00001101011110010(10000)110... - the binary representation of 17 (10001) is missing, - hence a(19) = 16. PROG (PARI) See Links section. CROSSREFS Cf. A144016, A300653, A300630. Sequence in context: A277561 A317684 A127973 * A023157 A228849 A069733 Adjacent sequences:  A300651 A300652 A300653 * A300655 A300656 A300657 KEYWORD nonn,base AUTHOR Rémy Sigrist, Mar 10 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)