A361390 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is carryless n^k base 10.
1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 4, 3, 1, 0, 1, 8, 9, 4, 1, 0, 1, 6, 7, 6, 5, 1, 0, 1, 2, 1, 4, 5, 6, 1, 0, 1, 4, 3, 6, 5, 6, 7, 1, 0, 1, 8, 9, 4, 5, 6, 9, 8, 1, 0, 1, 6, 7, 6, 5, 6, 3, 4, 9, 1, 0, 1, 2, 1, 4, 5, 6, 1, 2, 1, 10, 1, 0, 1, 4, 3, 6, 5, 6, 7, 6, 9, 100, 11, 1, 0, 1, 8, 9, 4, 5, 6, 9, 8, 1, 1000, 121, 12, 1
Offset: 0
Examples
4 * 4 = 16, so T(4,2) = 6. 6 * 4 = 24, so T(4,3) = 4. Square array begins: 1, 0, 0, 0, 0, 0, 0, 0, ... 1, 1, 1, 1, 1, 1, 1, 1, ... 1, 2, 4, 8, 6, 2, 4, 8, ... 1, 3, 9, 7, 1, 3, 9, 7, ... 1, 4, 6, 4, 6, 4, 6, 4, ... 1, 5, 5, 5, 5, 5, 5, 5, ... 1, 6, 6, 6, 6, 6, 6, 6, ... 1, 7, 9, 3, 1, 7, 9, 3, ...
Links
- Seiichi Manyama, Antidiagonals n = 0..139, flattened
- David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
- Index entries for sequences related to carryless arithmetic
Crossrefs
Programs
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PARI
T(n, k) = fromdigits(Vec(Pol(digits(n))^k)%10);