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A242166 Table T(d,n) of smallest k>1 such that binomial(k*n-1,n-1) == 1 (mod n^d), read by antidiagonals. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)