A060154 -id:A060154 - cp's OEIS frontend

A060155 Table T(n,k) by antidiagonals of floor(n^k/k) [n,k >= 1].

1, 0, 2, 0, 2, 3, 0, 2, 4, 4, 0, 4, 9, 8, 5, 0, 6, 20, 21, 12, 6, 0, 10, 48, 64, 41, 18, 7, 0, 18, 121, 204, 156, 72, 24, 8, 0, 32, 312, 682, 625, 324, 114, 32, 9, 0, 56, 820, 2340, 2604, 1555, 600, 170, 40, 10, 0, 102, 2187, 8192, 11160, 7776, 3361, 1024, 243, 50, 11

Offset: 1

Henry Bottomley, Mar 12 2001

			T(5,3)=[5^3/3]=[125/3]=41.
Rows start:
  1,  0,  0,   0,   0, ...
  2,  2,  2,   4,   6, ...
  3,  4,  9,  20,  48, ...
  4,  8, 21,  64, 204, ...
  5, 12, 41, 156, 625, ...

Seiichi Manyama, Antidiagonals n = 1..140, flattened

Rows include A000007, A000799, A092763, A129794, A129795, A129796, A129797, A129798, A129799, A060156.
Columns include A000027, A007590.
Diagonals include A000169.

T(n, k) = (A051129(n, k)-A060154(n, k))/k.

A062172 Table T(n,k) by antidiagonals of n^(k-1) mod k [n,k > 0].

Original entry on oeis.org

0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 3, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 1, 0, 1, 0, 1, 0, 1, 4, 0, 0, 1, 0, 0, 1, 4, 3, 1, 5, 1, 3, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 3, 7, 5, 1, 1, 1, 1, 1, 1, 0, 1, 8, 1, 4, 7, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 5, 0, 7, 1, 3, 0, 3, 0, 1, 0

Offset: 1

Henry Bottomley, Jun 12 2001

			T(5,3)=5^(3-1) mod 3=25 mod 3=1. Rows start (0,1,1,1,1,...), (0,0,1,0,1,...), (0,1,0,3,1...), (0,0,1,0,1,...), (0,1,1,1,0,...), ...

Cf. A002997, A060154. Rows include A057427, A062173, A062174, A062175, A062176. Columns include A000004, A000035, A011655, A010684 with interleaved 0's, A011558, A010875. Diagonals include all the rows again and A000004 and A009001 unsigned.

A114448 Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).

Original entry on oeis.org

0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 3, 4, 1, 0, 1, 0, 1, 4, 3, 2, 1, 0, 0, 1, 0, 0, 4, 3, 0, 1, 0, 1, 2, 1, 1, 1, 4, 1, 8, 1, 0, 0, 0, 0, 2, 0, 5, 0, 0, 4, 1, 0, 1, 1, 1, 3, 1, 6, 1, 1, 9, 2, 1, 0, 0, 2, 0, 4, 4, 0, 0, 8, 6, 3, 4, 1, 0, 1, 0, 1, 0, 3, 1, 1, 0, 5, 4, 9, 2, 1

Offset: 1

Leroy Quet, Feb 14 2006

Alternate description: triangular array a(n, k) = n^k (mod k) read by rows (n > 1, 0 < k < n). This is equivalent because a(n, k) = a(n-k, k). - David Wasserman, Jan 25 2007

			2^6 = 64 and 64 (mod 6) is 4. So a(2,6) = 4.

Cf. A051127, A051128, A094263. Transpose of A060154. First 13 rows are A057427(n-1), A015910, A066601, A066602, A066603, A066604, A066438, A066439, A066440, A056969, A066441, A066442, A116609. First 12 columns are A000004, A000035, A010872, A000035, A010874, A070431, A010876, A000035, A021559(n+1), A008959, A010880, A070435.

a[n_, k_] := Mod[n^k, k]; Table[a[n - k + 1, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 12 2012 *)

More terms from David Wasserman, Jan 25 2007

cp's OEIS Frontend

A060155 Table T(n,k) by antidiagonals of floor(n^k/k) [n,k >= 1].

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A062172 Table T(n,k) by antidiagonals of n^(k-1) mod k [n,k > 0].

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A114448 Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).

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