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

1,1

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Rémy Sigrist, Colored representation of the first 512 rows

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

Cf. A052410, A360963.

Sequence in context: A046921 A262954 A262813 * A188794 A161966 A187188

Adjacent sequences: A360961 A360962 A360963 * A360965 A360966 A360967

Keyword

nonn,base,tabl

Author

Rémy Sigrist, Feb 27 2023

Status

approved