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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.
3
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
1,6
COMMENTS
Leading zeros are ignored (and 0 is assumed to have binary length 0).
LINKS
Rémy Sigrist, Table of n, a(n) for n = 1..10011 (rows for n = 1..141 flattened)
FORMULA
T(n, 0) = 1.
T(n, n-1) = A183200(n-1) for n > 1.
EXAMPLE
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
PROG
(PARI) T(n, k) = { for (e=1, oo, if (#binary(n^e) != #binary(k^e), return (e))) }
CROSSREFS
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Feb 27 2023
STATUS
approved