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

0,9

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

Example

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, ...

Prog

(PARI) T(n, k) = fromdigits(Vec(Pol(digits(n))^k)%10);

Crossrefs

Columns k=0..4 give A000012, A001477, A059729, A169885, A169886.

Rows n=0..4 give A000007, A000012, A000689, A001148, A168428.

T(11,k) gives A059734.

Main diagonal gives A361351.

Cf. A004248, A359697.

Sequence in context: A048723 A364386 A088455 * A369326 A369324 A004248

Adjacent sequences: A361387 A361388 A361389 * A361391 A361392 A361393

Keyword

nonn,tabl,base

Author

Seiichi Manyama, Mar 10 2023

Status

approved