A360963 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.
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, 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, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3
Offset: 1
Examples
Triangle T(n, k) begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
----+-------------------------------------------------
1 | 1
2 | 1 1
3 | 1 1 2
4 | 1 1 1 1
5 | 1 1 1 1 4
6 | 1 1 1 1 2 2
7 | 1 1 1 1 2 2 3
8 | 1 1 1 1 1 1 1 1
9 | 1 1 1 1 1 1 1 1 6
10 | 1 1 1 1 1 1 1 1 4 4
11 | 1 1 1 1 1 1 1 1 3 3 3
12 | 1 1 1 1 1 1 1 1 2 2 2 2
13 | 1 1 1 1 1 1 1 1 2 2 2 2 3
14 | 1 1 1 1 1 1 1 1 2 2 2 2 3 4
15 | 1 1 1 1 1 1 1 1 2 2 2 2 3 4 6
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141 flattened)
- Rémy Sigrist, Colored representation of the first 512 rows
Programs
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PARI
T(n,k) = { for (e=1, oo, if (#binary(n^e) != #binary(k^e), return (e))) }
Formula
T(n, 0) = 1.
T(n, n-1) = A183200(n-1) for n > 1.
Comments