A216653 Number A(n,k) of n-digit k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals.

10, 4, 90, 3, 6, 900, 2, 2, 22, 9000, 2, 2, 5, 68, 90000, 2, 1, 2, 12, 217, 900000, 2, 1, 1, 4, 25, 683, 9000000, 2, 0, 1, 3, 8, 53, 2163, 90000000, 2, 0, 1, 1, 3, 14, 116, 6837, 900000000, 2, 0, 1, 1, 2, 6, 25, 249, 21623, 9000000000

Offset

1,1

Links

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Example

A(1,1) = 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
A(1,2) = 4: 0, 1, 4, 9.
A(2,2) = 6: 16, 25, 36, 49, 64, 81.
A(3,3) = 5: 125, 216, 343, 512, 729.
A(4,4) = 4: 1296, 2401, 4096, 6561.
A(5,5) = 3: 16807, 32768, 59049.
A(6,6) = 3: 117649, 262144, 531441.
Square array A(n,k) begins:
:n\k|        1:     2:    3:   4:   5:  6:  7:  8
+---+--------------------------------------------
: 1 |       10,     4,    3,   2,   2,  2,  2,  2
: 2 |       90,     6,    2,   2,   1,  1,  0,  0
: 3 |      900,    22,    5,   2,   1,  1,  1,  1
: 4 |     9000,    68,   12,   4,   3,  1,  1,  1
: 5 |    90000,   217,   25,   8,   3,  2,  2,  1
: 6 |   900000,   683,   53,  14,   6,  3,  2,  1
: 7 |  9000000,  2163,  116,  25,  10,  5,  2,  2
: 8 | 90000000,  6837,  249,  43,  14,  7,  4,  2

Maple

r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k<n, 1, 0) end:
A:= (n, k)-> r(10^n, k) -r(10^(n-1), k) +`if`(n=1, 1, 0):
seq(seq(A(n, 1+d-n), n=1..d), d=1..10);

Crossrefs

Columns k=1-10 give: A063945, A062940, A062941, A102831, A216655, A216656, A216657, A216658, A216659, A216654.

Main diagonal gives: A102690.

Sequence in context: A192027 A180866 A232908 * A267180 A038306 A317597

Adjacent sequences: A216650 A216651 A216652 * A216654 A216655 A216656

Keyword

nonn,tabl,base

Author

Alois P. Heinz, Sep 12 2012

Status

approved