A242166 Table T(d,n) of smallest k>1 such that binomial(k*n-1,n-1) == 1 (mod n^d), read by antidiagonals.

2, 2, 2, 2, 3, 2, 3, 2, 5, 2, 2, 9, 3, 9, 2, 4, 2, 33, 9, 17, 2, 2, 28, 2, 129, 27, 33, 2, 5, 2, 244, 5, 513, 81, 65, 2, 2, 33, 2, 1540, 25, 2049, 243, 129, 2, 6, 9, 257, 7, 4132, 125, 8193, 729, 257, 2, 2, 51, 81, 2049, 49, 66340, 625, 32769, 2187, 513, 2, 17, 2, 376, 729, 16385, 343, 159652, 3125, 131073, 6561, 1025, 2, 2, 161, 2, 4376, 6561, 131073, 2401, 1279396, 15625

Offset

1,1

Links

Table of n, a(n) for n=1..87.

Example

T(3,6) = 244, since k=244 is the smallest solution greater than 1 to the congruence binomial(k*6-1,6-1) == 1 (mod 6^3).
Table starts with:
  d=1: 2 2 2 3 2 4 2 5 2 ...
  d=2: 2 3 2 9 2 28 2 33 9 ...
  d=3: 2 5 3 33 2 244 2 257 81 ...
  d=4: 2 9 9 129 5 1540 7 2049 729 ...
  d=5: 2 17 27 513 25 4132 49 16385 6561 ...
  d=6: 2 33 81 2049 125 66340 343 131073 59049 ...
  d=7: 2 65 243 8193 625 159652 2401 ...
  ...

Crossrefs

Sequence in context: A216325 A322868 A240975 * A068211 A236832 A089050

Adjacent sequences: A242163 A242164 A242165 * A242167 A242168 A242169

Keyword

hard,nonn,tabl

Author

Felix Fröhlich and Max Alekseyev, May 05 2014

Status

approved