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A133906 Least number m such that binomial(n+m, m) mod m = 1.

%I A133906 #24 Aug 06 2018 15:19:14
%S A133906 2,3,5,2,2,7,9,2,2,3,3,2,2,17,17,2,2,3,3,2,2,23,25,2,2,4,3,2,2,31,37,
%T A133906 2,2,8,8,2,2,3,41,2,2,4,4,2,2,3,3,2,2,5,5,2,2,3,3,2,2,4,4,2,2,67,3,2,
%U A133906 2,44,44,2,2,16,16,2,2,3,4,2,2,5,5,2,2,3,3,2,2,89,9,2,2,3,3,2,2,97,97,2,2,7
%N A133906 Least number m such that binomial(n+m, m) mod m = 1.
%H A133906 Seiichi Manyama, <a href="/A133906/b133906.txt">Table of n, a(n) for n = 1..1000</a>
%e A133906 a(1)=2, since binomial(1+2, 2) mod 2 = 3 mod 2 = 1 and 2 is the minimal number with this property.
%e A133906 a(7)=9 because of binomial(7+9, 9) = 11440 = 1271*9 + 1, but binomial(7+k, k) mod k <> 1 for all numbers < 9.
%t A133906 Table[Block[{m = 1}, While[Mod[Binomial[n + m, m], m] != 1, m++]; m], {n, 98}] (* _Michael De Vlieger_, Jul 30 2018 *)
%o A133906 (PARI) a(n) = {my(m = 1, ok = 0); until (ok, if (binomial(n+m, m) % m == 1, ok = 1, m++);); return (m);} \\ _Michel Marcus_, Jul 15 2013
%Y A133906 Cf. A000040, A133620, A133621, A133623, A133630, A133635.
%Y A133906 Cf. A133872, A133880, A133890, A133900, A133907, A133910.
%K A133906 nonn
%O A133906 1,1
%A A133906 _Hieronymus Fischer_, Oct 20 2007