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.

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

Author

Rémy Sigrist, Feb 27 2023

Keywords

• nonn
• base
• tabl

Comments

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

Examples

			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
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10011
• Rémy Sigrist, Colored representation of the first 512 rows

Crossrefs

Cf. A052410, A360963.

Programs

PARI

T(n,k) = { for (b=2, oo, if (#digits(n,b) != #digits(k,b), return (b))) }

Formula

T(n, 0) = 2.

T(n, n-1) = A052410(n) for any n > 1.