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
Examples
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
Links
- Alois P. Heinz, Antidiagonals n = 1..141, flattened
Crossrefs
Programs
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Maple
r:= proc(n, k) local b; b:= iroot(n, k); b+`if`(b^k