cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A304879 a(n) = denominator(min{r with r in R}) and R = {0 <= r rational <= 1 and [r*k] = n}. Here k = 10^(floor(log_10(n))+1) and [x] = floor(x+1/2) + ceiling((2*x-1)/4) - floor((2*x-1)/4) - 1.

Original entry on oeis.org

1, 10, 6, 7, 8, 2, 9, 3, 4, 7, 21, 19, 26, 95, 37, 62, 58, 6, 40, 27, 41, 39, 93, 71, 17, 53, 98, 83, 40, 7, 61, 59, 73, 83, 98, 84, 76, 63, 8, 96, 81, 79, 53, 87, 85, 92, 90, 43, 40, 68, 2, 99, 33, 99, 71, 11, 9, 23, 40, 94, 42, 38, 13, 99, 74, 31, 29, 3, 40
Offset: 0

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Author

Peter Luschny, May 20 2018

Keywords

Comments

a(n) is the denominator of the smallest nonnegative fraction r such that round(10^d*r) = n, where d is the number of digits of n and Gaussian rounding (round half to even) is applied.

Examples

			The table below shows the different rational numbers which satisfy the requirements of the definition except minimality. The denominators of the first rational number in each row constitute the sequence. Note that the round function is not implemented uniformly in popular software. For example, Mathematica  matches our definition, while Maple's round function would return incorrect values.
.
  n | rational numbers       decimal value   rounded(10*r)
----+---------------------------------------------------
  0 | 0/1,                   .0000000000,         0
  1 | 1/10, 1/9, 1/8, 1/7,   .1000000000,         1
  2 | 1/6, 1/5, 2/9, 1/4,    .1666666667,         2
  3 | 2/7, 3/10, 1/3,        .2857142857,         3
  4 | 3/8, 2/5, 3/7, 4/9,    .3750000000,         4
  5 | 1/2,                   .5000000000,         5
  6 | 5/9, 4/7, 3/5, 5/8,    .5555555556,         6
  7 | 2/3, 7/10, 5/7,        .6666666667,         7
  8 | 3/4, 7/9, 4/5, 5/6,    .7500000000,         8
  9 | 6/7, 7/8, 8/9, 9/10,   .8571428571,         9
		

Crossrefs

Cf. A304880 (numerators), A303612.

Programs

  • Maple
    r := proc(n) local nint, k, p, q, S; k := 10^(ilog10(n)+1);
    nint := m -> floor(m + 1/2) +  ceil((2*m-1)/4) - floor((2*m-1)/4) - 1;
    if n = 0 then return 0/1 fi; S := NULL;
    for p from 1 to k do for q from p+1 to k do
        if nint(p*k/q) = n then S := S,p/q fi
    od od; sort(convert({S}, list))[1] end:
    a := n -> denom(r(n)): seq(a(n), n=0..68);
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