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 1-3 of 3 results.

A350601 Array read by antidiagonals: row n lists even numbers that are "generated" (in Kaprekar's sense) in all bases 2, 4, 6, ..., 2n.

Original entry on oeis.org

0, 0, 2, 0, 2, 8, 0, 2, 10, 10, 0, 2, 10, 12, 12, 0, 2, 10, 14, 14, 14, 0, 2, 10, 14, 16, 16, 16, 0, 2, 10, 14, 22, 22, 22, 20, 0, 2, 10, 14, 22, 24, 24, 24, 22, 0, 2, 10, 14, 22, 24, 28, 28, 26, 24
Offset: 1

Views

Author

N. J. A. Sloane, Jan 08 2022

Keywords

Comments

Max Alekseyev's PARI "Gen" program (see A010061) is essential for computing the rows. Cf. A349833.

Examples

			The initial rows of the array are:
  0, 2,  8, 10, 12, 14, 16, 20, 22, 24, 26, 28, 34, 36, 38, 40, 42, 44, 50, 52,  ... [the even terms of A228082]
  0, 2, 10, 12, 14, 16, 22, 24, 26, 28, 34, 36, 38, 40, 44, 50, 58, 60, 62, 66  ... [A349831]
  0, 2, 10, 14, 16, 22, 24, 28, 34, 36, 38, 44, 50, 58, 60, 62, 66, 68, 72, 74,  ... [A349832]
  0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84,  ... [A349833]
  0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84,  ...
  0, 2, 10, 14, 22, 28, 36, ...
  0, 2, 10, 14, 22, 36, ...
  0, 2, 10, 14, 22, 36,...
  0, 2, 10, 14, 22, ...
...
The rows converge to A230624, which is
  0, 2, 10, 14, 22, 38, 62, 94, 158, 206, 318, 382, 478, 606, 766, 958, 1022, ...
The initial antidiagonals are:
  0,
  0, 2,
  0, 2, 8,
  0, 2, 10, 10,
  0, 2, 10, 12, 12,
  0, 2, 10, 14, 14, 14,
  0, 2, 10, 14, 16, 16, 16,
  0, 2, 10, 14, 22, 22, 22, 20,
  0, 2, 10, 14, 22, 24, 24, 24, 22,
  0, 2, 10, 14, 22, 24, 28, 28, 26, 24,
  ...

Links

Crossrefs

The first few rows of the array are A228082 (even terms only), A349831, A349832, and A349833.
Cf. A003052, A010061, A230624.

Extensions

[Needs checking and extending]

A349831 Even numbers in the intersection of A228082 and A349829.

Original entry on oeis.org

0, 2, 10, 12, 14, 16, 22, 24, 26, 28, 34, 36, 38, 40, 44, 50, 58, 60, 62, 66, 68, 70, 72, 74, 76, 82, 84, 92, 94, 96, 98, 106, 108, 110, 114, 118, 120, 122, 126, 132, 134, 136, 140, 146, 154, 156, 158, 162, 164, 170, 174, 176, 178, 186, 188, 190, 196, 198, 202, 204, 206, 210, 214, 216, 218, 222
Offset: 1

Views

Author

N. J. A. Sloane, Jan 07 2022

Keywords

Comments

Even numbers that are "generated" (in Kaprekar's sense) in both bases 2 and 4.

Crossrefs

Cf. A003052, A228082, A349829, A349830, A349832.
A230624 is a subsequence.
A row of A350601.

A349833 Even numbers that are "generated" (in Kaprekar's sense) in all four bases 2, 4, 6, and 8.

Original entry on oeis.org

0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84, 92, 94, 96, 98, 106, 110, 118, 120, 122, 132, 134, 136, 140, 154, 156, 158, 162, 170, 176, 178, 186, 196, 198, 206, 210, 214, 216, 222, 228, 234, 244, 246, 252, 258, 260, 262, 264, 268, 274, 284, 286
Offset: 1

Views

Author

N. J. A. Sloane, Jan 07 2022

Keywords

Comments

Using Max Alekseyev's PARI "Gen" program (see A010061), we run
vector(500,k,length(Gen(k,2))),
vector(500,k,length(Gen(k,4))),
vector(500,k,length(Gen(k,6))),
vector(500,k,length(Gen(k,8))),
to find the numbers that are generated in bases 2, 4, 6, and 8, and then take the even numbers that are common to all four lists.

Links

Crossrefs

Cf. A003052, A010061, A228082, A349829, A349830, A349831, A349832.
A230624 is a subsequence.
A row of A350601.
Showing 1-3 of 3 results.

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

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