A360964 - OEIS

%I #10 Mar 01 2023 02:09:06

%S 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,

%T 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,

%U 2,2,2,2,2,2,2,3,10,11,12,2,2,2,2,2,2,2,2,3,10,11,12,13

%N 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.

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

%H Rémy Sigrist, <a href="/A360964/b360964.txt">Table of n, a(n) for n = 1..10011</a>

%H Rémy Sigrist, <a href="/A360964/a360964.png">Colored representation of the first 512 rows</a>

%F T(n, 0) = 2.

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

%e Triangle T(n, k) begins:

%e   n\k | 0  1  2  3  4  5  6  7  8   9  10  11

%e   ----+--------------------------------------

%e     1 | 2

%e     2 | 2  2

%e     3 | 2  2  3

%e     4 | 2  2  2  2

%e     5 | 2  2  2  2  5

%e     6 | 2  2  2  2  5  6

%e     7 | 2  2  2  2  5  6  7

%e     8 | 2  2  2  2  2  2  2  2

%e     9 | 2  2  2  2  2  2  2  2  3

%e    10 | 2  2  2  2  2  2  2  2  3  10

%e    11 | 2  2  2  2  2  2  2  2  3  10  11

%e    12 | 2  2  2  2  2  2  2  2  3  10  11  12

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

%Y Cf. A052410, A360963.

%K nonn,base,tabl

%O 1,1

%A _Rémy Sigrist_, Feb 27 2023