A063432 Triangle read by rows in which k-th entry in row n is representation of n in base k, for 1 <= k <= n.

1, 11, 10, 111, 11, 10, 1111, 100, 11, 10, 11111, 101, 12, 11, 10, 111111, 110, 20, 12, 11, 10, 1111111, 111, 21, 13, 12, 11, 10, 11111111, 1000, 22, 20, 13, 12, 11, 10, 111111111, 1001, 100, 21, 14, 13, 12, 11, 10, 1111111111, 1010, 101, 22, 20, 14, 13

Offset

1,2

Comments

Representation of n in base 1 is defined to be a concatenation of n 1's.

It is difficult to write twenty-one in base 11 using decimal digits.

Representation in bases greater than 10 are written in base 10. This is really nasty! - N. J. A. Sloane, Dec 06 2002

Links

Table of n, a(n) for n=1..52.

Example

Rows start (1), (11, 10), (111, 11, 10), (1111, 100, 11, 10), etc.

Mathematica

f[n_] := Flatten[ Append[ {FromDigits[ Table[1, {n}]] }, Table[ FromDigits[ IntegerDigits[n, i]], {i, 2, n}]]]; Flatten[ Table[ f[n], {n, 1, 10}]] (* Robert G. Wilson v *)

Crossrefs

Cf. A063431.

Rows are effectively the reverse of A001731, A001732, A001733, A001734, A001735, A001736, A008707, A008708, A008709, A008710, A008711, A008712, A008713, A008714, A008715, A008716, A008717, etc.

Columns are truncated versions of A000042, A007088, A007089, A007090, A007091, A007092, A007093, A007094, A007095, A000027 and perhaps A055649, etc.

Without the 1st column becomes A004053.

Sequence in context: A014550 A367547 A070836 * A364121 A038324 A164125

Adjacent sequences: A063429 A063430 A063431 * A063433 A063434 A063435

Keyword

base,nonn,tabl

Author

Henry Bottomley, Jul 20 2001

Status

approved