

A317872


a(n) is the number of times that binomial(n+m, m) mod m = 1, for 0 < m <= n.


1



0, 0, 0, 1, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 0, 2, 2, 1, 1, 3, 2, 0, 0, 1, 2, 2, 4, 4, 4, 0, 0, 3, 4, 1, 1, 3, 3, 1, 0, 1, 1, 2, 2, 1, 2, 1, 1, 2, 4, 2, 2, 4, 4, 6, 4, 3, 2, 2, 2, 1, 1, 0, 1, 7, 6, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 3, 7, 4, 4, 4, 4, 0, 1, 2, 2, 2, 2, 2, 1, 0, 0, 3, 3, 3, 4, 5, 5, 2, 2, 3, 1
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OFFSET

1,9


COMMENTS

First occurrence of k with k = 0, 1, 2,...: 1, 4, 10, 9, 27, 100, 54, 64, 176, 544, 352, 648, 649, 129, 128, 1378, 513, 729, 7776, 1377, 5832, 1701, 3728, 13312, 13825, ...
Records: 0, 1, 3, 4, 6, 7, 14, 16, 17, 19, 21, 22, ..., ; and they occur at: 1, 4, 9, 27, 54, 64, 128, 513, 729, 1377, 1701, 3728, 6656, ...


LINKS



EXAMPLE

a(9) = 3 because binomial(9+2,2) mod 2 = binomial(9+3,3) mod 3 = binomial(9+6,6) mod 6 = 1. [Corrected by Jon E. Schoenfield, Aug 28 2018]


MATHEMATICA

a[n_] := Block[{c = 0, m = 1}, While[m < n + 1, If[ Mod[ Binomial[n + m, m], m] == 1, c++]; m++]; c]; Array[a, 105]
Table[Count[Table[Mod[Binomial[n+m, m], m], {m, n}], 1], {n, 120}] (* Harvey P. Dale, Aug 18 2022 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



