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Array read by antidiagonals: row n lists even numbers that are "generated" (in Kaprekar's sense) in all bases 2, 4, 6, ..., 2n.
5

%I #9 Jan 08 2022 22:08:50

%S 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,

%T 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,

%U 28,26,24

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

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

%H <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>

%e The initial rows of the array are:

%e 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]

%e 0, 2, 10, 12, 14, 16, 22, 24, 26, 28, 34, 36, 38, 40, 44, 50, 58, 60, 62, 66 ... [A349831]

%e 0, 2, 10, 14, 16, 22, 24, 28, 34, 36, 38, 44, 50, 58, 60, 62, 66, 68, 72, 74, ... [A349832]

%e 0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84, ... [A349833]

%e 0, 2, 10, 14, 22, 24, 28, 36, 38, 44, 50, 58, 60, 62, 66, 68, 74, 76, 82, 84, ...

%e 0, 2, 10, 14, 22, 28, 36, ...

%e 0, 2, 10, 14, 22, 36, ...

%e 0, 2, 10, 14, 22, 36,...

%e 0, 2, 10, 14, 22, ...

%e ...

%e The rows converge to A230624, which is

%e 0, 2, 10, 14, 22, 38, 62, 94, 158, 206, 318, 382, 478, 606, 766, 958, 1022, ...

%e The initial antidiagonals are:

%e 0,

%e 0, 2,

%e 0, 2, 8,

%e 0, 2, 10, 10,

%e 0, 2, 10, 12, 12,

%e 0, 2, 10, 14, 14, 14,

%e 0, 2, 10, 14, 16, 16, 16,

%e 0, 2, 10, 14, 22, 22, 22, 20,

%e 0, 2, 10, 14, 22, 24, 24, 24, 22,

%e 0, 2, 10, 14, 22, 24, 28, 28, 26, 24,

%e ...

%Y The first few rows of the array are A228082 (even terms only), A349831, A349832, and A349833.

%Y Cf. A003052, A010061, A230624.

%K nonn,tabl,more

%O 1,3

%A _N. J. A. Sloane_, Jan 08 2022

%E [Needs checking and extending]