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A360964
Triangle T(n, k), n > 0, k = 0..n-1, read by rows: T(n, k) is the least base b >= 2 where the number of digits of n and k are different.
3
2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 5, 6, 2, 2, 2, 2, 5, 6, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 10, 2, 2, 2, 2, 2, 2, 2, 2, 3, 10, 11, 2, 2, 2, 2, 2, 2, 2, 2, 3, 10, 11, 12, 2, 2, 2, 2, 2, 2, 2, 2, 3, 10, 11, 12, 13
OFFSET
1,1
COMMENTS
Leading zeros are ignored (and 0 is assumed to have length 0).
FORMULA
T(n, 0) = 2.
T(n, n-1) = A052410(n) for any n > 1.
EXAMPLE
Triangle T(n, k) begins:
n\k | 0 1 2 3 4 5 6 7 8 9 10 11
----+--------------------------------------
1 | 2
2 | 2 2
3 | 2 2 3
4 | 2 2 2 2
5 | 2 2 2 2 5
6 | 2 2 2 2 5 6
7 | 2 2 2 2 5 6 7
8 | 2 2 2 2 2 2 2 2
9 | 2 2 2 2 2 2 2 2 3
10 | 2 2 2 2 2 2 2 2 3 10
11 | 2 2 2 2 2 2 2 2 3 10 11
12 | 2 2 2 2 2 2 2 2 3 10 11 12
PROG
(PARI) T(n, k) = { for (b=2, oo, if (#digits(n, b) != #digits(k, b), return (b))) }
CROSSREFS
Sequence in context: A046921 A262954 A262813 * A188794 A161966 A187188
KEYWORD
nonn,base,tabl
AUTHOR
Rémy Sigrist, Feb 27 2023
STATUS
approved