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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

%I

%S 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,

%T 244,5,513,81,65,2,2,33,2,1540,25,2049,243,129,2,6,9,257,7,4132,125,

%U 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

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

%e 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).

%e Table starts with:

%e d=1: 2 2 2 3 2 4 2 5 2 ...

%e d=2: 2 3 2 9 2 28 2 33 9 ...

%e d=3: 2 5 3 33 2 244 2 257 81 ...

%e d=4: 2 9 9 129 5 1540 7 2049 729 ...

%e d=5: 2 17 27 513 25 4132 49 16385 6561 ...

%e d=6: 2 33 81 2049 125 66340 343 131073 59049 ...

%e d=7: 2 65 243 8193 625 159652 2401 ...

%e ...

%K hard,nonn,tabl

%O 1,1

%A _Felix Fröhlich_ and _Max Alekseyev_, May 05 2014

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Last modified June 23 17:11 EDT 2021. Contains 345402 sequences. (Running on oeis4.)