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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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A249856 Let z = A084937: a(n) = number of odd numbers <= z(n) that are != z(k) for k=1..n-1 and not coprime to z(n-1) and z(n-2).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2, 3, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 4, 0, 2, 3, 0, 0, 4, 0, 0, 2, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 09 2014

Keywords

Comments

a(n) = A249777(n) - A249857(n).

Crossrefs

Cf. A084937, A249777, A249857, A249858.
For a different way to look at the missing numbers in A084937, see A249686, A250099, A250100.

Programs

  • Haskell
    a249856 = sum . map (flip mod 2) . (uss !!)
uss = [] : [] : [] : f 2 1 [3..] where
   f x y zs = g zs [] where
      g (v:vs) ws | gcd v y > 1 || gcd v x > 1 = g vs (v : ws)
                  | otherwise = ws : f v x (delete v zs)

A249857 Let z = A084937: a(n) = number of even numbers <= z(n) that are != z(k) for k=1..n-1 and not coprime to z(n-1) and z(n-2).

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 2, 1, 2, 3, 0, 4, 5, 0, 5, 6, 2, 2, 8, 1, 5, 6, 3, 7, 9, 0, 9, 11, 0, 11, 13, 0, 5, 13, 1, 10, 14, 1, 6, 14, 2, 11, 15, 4, 15, 16, 2, 16, 12, 5, 16, 17, 3, 17, 18, 0, 19, 20, 0, 21, 24, 0, 21, 24, 1, 15, 26, 3, 17, 24, 4, 19, 26, 2, 21, 26
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 09 2014

Keywords

Comments

a(n) = A249777(n) - A249856(n).

Examples

			.     |            |     unused even numbers <  A084937(n)    |
.   n | A084937(n) |     [uncounted odd terms in brackets]    | a(n)
. ----+------------+------------------------------------------+-----
.   3 |          3 |  _                                       |    0
.   4 |          5 |  4                                       |    1
.   5 |          4 |  _                                       |    0
.   6 |          7 |  6                                       |    1
.   7 |          9 |  6,8                                     |    2
.   8 |          8 |  6                                       |    1
.   9 |         11 |  6,10                                    |    2
.  10 |         13 |  6,10,12                                 |    3
.  11 |          6 |  _                                       |    0
.  12 |         17 |  10,12,14,[15],16                        |    4
.  13 |         19 |  10,12,14,[15],16,18                     |    5
.  14 |         10 |  _                                       |    0
.  15 |         21 |  12,14,[15],16,18,20                     |    5
.  16 |         23 |  12,14,[15],16,18,20,22                  |    6
.  17 |         16 |  12,14,[15]                              |    2
.  18 |         15 |  12,14                                   |    2
.  19 |         29 |  12,14,18,20,22,24,[25],26,[27],28       |    8
.  20 |         14 |  12                                      |    1
.  21 |         25 |  12,18,20,22,24                          |    5
.  22 |         27 |  12,18,20,22,24,26                       |    6
.  23 |         22 |  12,18,20                                |    3
.  24 |         31 |  12,18,20,24,26,28,30                    |    7
.  25 |         35 |  12,18,20,24,26,28,30,32,[33],34         |    9 .

Crossrefs

Cf. A084937, A249777, A249856, A249858.
For a different way to look at the missing numbers in A084937, see A249686, A250099, A250100.

Programs

  • Haskell
    a249857 = sum . map ((1 -) . flip mod 2) . (uss !!)
-- See A249856 for definition of uss.

A249686 After A084937(n) has been computed, let m = largest term so far in A084937. Then a(n) = number of positive integers < m that are missing from A084937 at this point.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 2, 1, 2, 3, 2, 5, 6, 5, 6, 7, 6, 5, 10, 9, 8, 7, 6, 7, 10, 9, 10, 13, 12, 13, 16, 15, 14, 15, 14, 13, 16, 15, 14, 15, 14, 13, 16, 15, 16, 17, 16, 17, 16, 15, 16, 17, 16, 17, 18, 17, 20, 21, 20, 23, 28, 27, 26, 27, 26, 25, 30, 29, 28, 27, 26, 25, 28
Offset: 1

Views

Author

N. J. A. Sloane, Nov 05 2014

Keywords

Comments

Running count of missing numbers in A084937.
It appears that at any point, the number of missing even numbers from A084937 is always much larger than the number of missing odd numbers. It would be nice to have a more precise statement of this property.
In this regard, it would be helpful to have two further sequences, one giving the number of even missing numbers at each point, the other giving the number of odd missing numbers. These are now A250099, A250100. See also A249777, A249856, A249867.

Examples

			After step 7 of A084937, here is what we have:
1 2 3 4 5 6 7 ... n
1 2 3 5 4 7 9 ... A084937(n)
so m = 9, and the missing numbers < 9 are 6 and 8, so a(7) = 2.

Links

Crossrefs

Cf. A084937, A250099, A250100. See A249777, A249856, A249857, A249858 for another way of looking at this question.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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