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A216653
Number A(n,k) of n-digit k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals.
12
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
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
Main diagonal gives: A102690.
Sequence in context: A192027 A180866 A232908 * A267180 A038306 A317597
KEYWORD
nonn,tabl,base
AUTHOR
Alois P. Heinz, Sep 12 2012
STATUS
approved