A138028 The array of the most significant digit of n^k read by antidiagonals.

1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 9, 8, 1, 1, 5, 1, 2, 1, 1, 1, 6, 2, 6, 8, 3, 1, 1, 7, 3, 1, 2, 2, 6, 1, 1, 8, 4, 2, 6, 1, 7, 1, 1, 1, 9, 6, 3, 1, 3, 4, 2, 2, 1, 1, 1, 8, 5, 2, 7, 1, 1, 6, 5, 1, 1, 1, 1, 7, 4, 1, 4, 7, 6, 1, 1, 1, 1, 1, 1, 1, 6, 3, 1, 2, 3, 2, 5, 2, 1, 1, 1, 1, 1, 1, 5, 2, 8, 1, 1, 1, 1, 4, 1

Offset: 1

Author

Robert G. Wilson v, Feb 10 2008

Keywords

• base
• nonn
• tabl

Examples

			n\k
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... .
1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, 2, 4, 8, 1, 3, 6, 1, 2, 5, 1, ... .
1, 3, 9, 2, 8, 2, 7, 2, 6, 1, 5, 1, 5, 1, 4, 1, 4, 1, 3, 1, 3, ... .
1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, 4, 1, 6, 2, 1, ... .
1, 5, 2, 1, 6, 3, 1, 7, 3, 1, 9, 4, 2, 1, 6, 3, 1, 7, 3, 1, 9, ... .
1, 6, 3, 2, 1, 7, 4, 2, 1, 1, 6, 3, 2, 1, 7, 4, 2, 1, 1, 6, 3, ... .
1, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, 8, 6, 5, 4, 3, 2, 2, 1, 1, 1, ... .
1, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 1, ... .
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... .
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 6, ... .
1, 1, 1, 1, 2, 2, 2, 3, 4, 5, 6, 7, 8, 1, 1, 1, 1, 2, 2, 3, 3, ... .
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Crossrefs

Cf. A008952, A060956, A138029, A061505.

Programs

Mathematica

f[n_, k_] := Quotient[n^k, 10^Floor[k*Log[10, n]]]; Table[f[ n - k, k], {n, 14}, {k, 0, n - 1}] // Flatten