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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A322510 a(1) = 0, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) - k(n) where k(n) is the least positive integer not leading to a duplicate term in sequence a.

Original entry on oeis.org

0, 1, -1, 4, -2, 2, -4, 5, 3, 6, -10, 7, -3, 8, -16, 15, -5, 12, -6, 19, -7, -9, -11, 22, -8, 9, -15, 28, -12, -14, -18, 16, 14, 10, -20, 13, 11, 17, -29, 20, 18, 21, -35, 23, -41, 24, -46, 57, -13, 26, -42, 35, -17, 25, -55, 29, 27, 30, -54, 31, -59, 32, -68
Offset: 1

Views

Author

Rémy Sigrist, Dec 13 2018

Keywords

Comments

The point is that the same k(n) must be used for both a(2*n) and a(2*n+1). - N. J. A. Sloane, Dec 17 2019
Apparently every signed integer appears in the sequence.

Examples

			The first terms, alongside k(n) and associate children, are:
  n   a(n)  k(n)  a(2*n)  a(2*n+1)
  --  ----  ----  ------  --------
   1     0     1       1        -1
   2     1     3       4        -2
   3    -1     3       2        -4
   4     4     1       5         3
   5    -2     8       6       -10
   6     2     5       7        -3
   7    -4    12       8       -16
   8     5    10      15        -5
   9     3     9      12        -6
  10     6    13      19        -7

Links

Crossrefs

For k(n) see A330337, A330338.
See A305410, A304971 and A322574-A322575 for similar sequences.

Programs

  • PARI
    lista(nn) = my (a=[0], s=Set(0)); for (n=1, ceil(nn/2), for (k=1, oo, if (!setsearch(s, a[n]+k) && !setsearch(s, a[n]-k), a=concat(a, [a[n]+k, a[n]-k]); s=setunion(s, Set([a[n]+k, a[n]-k])); break))); a[1..nn]

Formula

a(n) = (a(2*n) + a(2*n+1))/2.

A322574 z(1) = 0, and for any n > 0, z(4*n-2) = z(n) + k(n), z(4*n-1) = z(n) + i*k(n), z(4*n) = z(n) - k(n) and z(4*n+1) = z(n) - i*k(n) where k(n) is the least positive integer not leading to a duplicate term in sequence z (and i denotes the imaginary unit); a(n) is the real part of z(n).

Original entry on oeis.org

0, 1, 0, -1, 0, 4, 1, -2, 1, 3, 0, -3, 0, 2, -1, -4, -1, 3, 0, -3, 0, 5, 4, 3, 4, 2, 1, 0, 1, 6, -2, -10, -2, 2, 1, 0, 1, 7, 3, -1, 3, 9, 0, -9, 0, -2, -3, -4, -3, 7, 0, -7, 0, 9, 2, -5, 2, 3, -1, -5, -1, 7, -4, -15, -4, 4, -1, -6, -1, 8, 3, -2, 3, 8, 0, -8, 0
Offset: 1

Views

Author

Rémy Sigrist, Dec 17 2018

Keywords

Comments

Will z run through every Gaussian integer?

Examples

			The first terms, alongside z(n), k(n) and associate children, are:
  n   a(n)  z(n)     k  z(4*n-2)  z(4*n-1)  z(4*n)  z(4*n+1)
  --  ----  -------  -  --------  --------  ------  --------
   1     0        0  1         1         i      -1        -i
   2     1        1  3         4   1 + 3*i      -2   1 - 3*i
   3     0        i  3     3 + i       4*i  -3 + i      -2*i
   4    -1       -1  3         2  -1 + 3*i      -4  -1 - 3*i
   5     0       -i  3     3 - i       2*i  -3 - i      -4*i
   6     4        4  1         5     4 + i       3     4 - i
   7     1  1 + 3*i  1   2 + 3*i   1 + 4*i     3*i   1 + 2*i
   8    -2       -2  8         6  -2 + 8*i     -10  -2 - 8*i
   9     1  1 - 3*i  1   2 - 3*i   1 - 2*i    -3*i   1 - 4*i
  10     3    3 + i  4     7 + i   3 + 5*i  -1 + i   3 - 3*i

Links

Crossrefs

See A322575 for the imaginary part of z.
This sequence is a complex variant of A322510.

Programs

  • PARI
    \\ See Links section.
Showing 1-2 of 2 results.

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

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