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 A300475 a(n) is the least positive k such that the binary representation n appears in front of the binary representation of 1/k (ignoring the radix point and the leading zeros and adding trailing zeros if necessary in case of a terminating expansion). 3
 1, 1, 5, 1, 3, 5, 9, 1, 7, 3, 11, 5, 19, 9, 17, 1, 15, 7, 13, 25, 3, 23, 11, 21, 5, 19, 37, 9, 35, 17, 33, 1, 31, 15, 29, 7, 27, 53, 13, 25, 49, 3, 47, 23, 45, 11, 43, 21, 41, 81, 5, 39, 19, 75, 37, 9, 71, 35, 69, 17, 67, 33, 65, 1, 63, 31, 61, 15, 59, 29, 57 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS In other words, a(n) is the least k > 0 such that floor((2^i) / k) = n for some integer i >= 0. This sequence is similar to A095156 for the base 2. All terms are odd. All terms appears infinitely many times (as a(n) equals at least a(2*n) or a(2*n + 1)). See also A300428 for a similar sequence. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A300475 Rémy Sigrist, Colored logarithmic scatterplot of the first 1000000 terms (where the color is function of A070939(n * a(n))) FORMULA a(2^k) = 1 for any k >= 0. a(2^k - 1) = 2^k + 1 for any k > 1. a(A000975(k)) = 3 for any k > 2. a(A033138(k)) = 7 for any k > 4. a(n) >= A300428(n). EXAMPLE The first terms, alongside the binary representation of 1/a(n) with the earliest occurrence of the binary representation of n in parentheses, are:   n  a(n)    bin(1/a(n))   -- ----    -----------    1    1    (1).000...    2    1    (1.0)000...    3    5    0.00(11)001...    4    1    (1.00)000...    5    3    0.0(101)010...    6    5    0.00(110)011...    7    9    0.000(111)000...    8    1    (1.000)000...    9    7    0.00(1001)001...   10    3    0.0(1010)101...   11   11    0.000(1011)101...   12    5    0.00(1100)110...   13   19    0.0000(1101)011...   14    9    0.000(1110)001...   15   17    0.0000(1111)000...   16    1    (1.0000)000...   17   15    0.000(10001)000...   18    7    0.00(10010)010...   19   13    0.000(10011)101...   20   25    0.0000(10100)011... PROG (PARI) See Links section. CROSSREFS Cf. A000975, A033138, A070939, A095156, A300428. Sequence in context: A327968 A213815 A300428 * A143113 A053544 A174879 Adjacent sequences:  A300472 A300473 A300474 * A300476 A300477 A300478 KEYWORD nonn,look,base AUTHOR Rémy Sigrist, Mar 06 2018 STATUS approved

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Last modified May 25 01:00 EDT 2022. Contains 354047 sequences. (Running on oeis4.)