login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Triangle T(n, k), n > 0, k = 0..n-1, read by rows: T(n, k) is the least e > 0 such that the binary expansions of n^e and k^e have different lengths.
3

%I #11 Mar 01 2023 02:09:13

%S 1,1,1,1,1,2,1,1,1,1,1,1,1,1,4,1,1,1,1,2,2,1,1,1,1,2,2,3,1,1,1,1,1,1,

%T 1,1,1,1,1,1,1,1,1,1,6,1,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,1,3,3,3,1,1,

%U 1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,1,2,2,2,2,3

%N Triangle T(n, k), n > 0, k = 0..n-1, read by rows: T(n, k) is the least e > 0 such that the binary expansions of n^e and k^e have different lengths.

%C Leading zeros are ignored (and 0 is assumed to have binary length 0).

%H Rémy Sigrist, <a href="/A360963/b360963.txt">Table of n, a(n) for n = 1..10011</a> (rows for n = 1..141 flattened)

%H Rémy Sigrist, <a href="/A360963/a360963.png">Colored representation of the first 512 rows</a>

%F T(n, 0) = 1.

%F T(n, n-1) = A183200(n-1) for n > 1.

%e Triangle T(n, k) begins:

%e n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

%e ----+-------------------------------------------------

%e 1 | 1

%e 2 | 1 1

%e 3 | 1 1 2

%e 4 | 1 1 1 1

%e 5 | 1 1 1 1 4

%e 6 | 1 1 1 1 2 2

%e 7 | 1 1 1 1 2 2 3

%e 8 | 1 1 1 1 1 1 1 1

%e 9 | 1 1 1 1 1 1 1 1 6

%e 10 | 1 1 1 1 1 1 1 1 4 4

%e 11 | 1 1 1 1 1 1 1 1 3 3 3

%e 12 | 1 1 1 1 1 1 1 1 2 2 2 2

%e 13 | 1 1 1 1 1 1 1 1 2 2 2 2 3

%e 14 | 1 1 1 1 1 1 1 1 2 2 2 2 3 4

%e 15 | 1 1 1 1 1 1 1 1 2 2 2 2 3 4 6

%o (PARI) T(n,k) = { for (e=1, oo, if (#binary(n^e) != #binary(k^e), return (e))) }

%Y Cf. A029837, A183200, A360964.

%K nonn,base,tabl

%O 1,6

%A _Rémy Sigrist_, Feb 27 2023