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.

Showing 1-4 of 4 results.

A330337 The sequence {k(n)} involved in the construction of A322510.

Original entry on oeis.org

1, 3, 3, 1, 8, 5, 12, 10, 9, 13, 1, 15, 12, 20, 2, 1, 15, 1, 23, 1, 28, 32, 35, 35, 34, 26, 40, 1, 42, 45, 50, 35, 35, 32, 53, 37, 34, 42, 1, 46, 45, 52, 1, 55, 2, 57, 1, 1, 47, 63, 2, 73, 53, 73, 2, 78, 77, 81, 2, 89, 96
Offset: 1

Views

Author

N. J. A. Sloane, Dec 17 2019

Keywords

Links

Crossrefs

Cf. A322510.

Formula

a(n) = A322510(2n)-A322510(n).

A305410 a(1) = 1, and for any n > 0, a(2*n) = a(n) + k(n) and a(2*n+1) = a(n) + 2 * k(n) where k(n) is the least positive integer not leading to a duplicate term.

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 13, 11, 15, 16, 24, 17, 22, 18, 26, 21, 28, 19, 29, 20, 27, 23, 35, 30, 45, 25, 34, 31, 38, 32, 47, 33, 44, 36, 54, 37, 48, 39, 57, 40, 52, 41, 63, 42, 55, 43, 66, 46, 65, 49, 75, 51, 67, 50, 70, 53, 61, 56, 87, 58, 82
Offset: 1

Views

Author

Rémy Sigrist, Dec 16 2018

Keywords

Comments

Apparently, every positive 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     1     1       2         3
   2     2     2       4         6
   3     3     2       5         7
   4     4     4       8        12
   5     6     4      10        14
   6     5     4       9        13
   7     7     4      11        15
   8     8     8      16        24
   9    12     5      17        22
  10    10     8      18        26

Links

Crossrefs

This sequence is a variant of A322510.

Programs

  • PARI
    lista(nn) = my (a=[1], s=2^a[1]); for (n=1, ceil(nn/2), for (k=1, oo, if (!bittest(s, a[n]+k) && !bittest(s, a[n]+2*k), a=concat(a, [a[n]+k, a[n]+2*k]); s+=2^(a[n]+k) + 2^(a[n]+2*k); break))); a[1..nn]

Formula

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

Extensions

Name corrected by Rémy Sigrist, Apr 26 2020

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.

A330338 Indices k such that A330337(k) = 1.

Original entry on oeis.org

1, 4, 11, 16, 18, 20, 28, 39, 43, 47, 48, 63, 68, 71, 80, 84, 88, 100, 108, 124, 151, 155, 171, 175, 187, 189, 196, 199, 215, 219, 223, 227, 237, 239, 243, 251, 253, 255, 271, 279, 280, 308, 312, 320, 332, 344, 348, 372, 376, 380, 400, 404, 416, 418, 420, 428, 432, 448, 450, 464, 480, 482, 484, 488, 496
Offset: 1

Views

Author

N. J. A. Sloane, Dec 17 2019

Keywords

Links

Crossrefs

Cf. A322510, A330337.
Showing 1-4 of 4 results.

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

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