A133905 - OEIS

%I #9 May 13 2022 15:01:01

%S 4,9,25,10,26,9,9,9,6,4,4,34,34,85,289,4,4,57,87,8,8,25,25,25,134,4,4,

%T 15,15,111,111,4,4,8,8,10,10,121,121,82,86,4,4,49,49,49,49,4,4,265,68,

%U 10,10,8,8,6,9,4,4,194,194,469,249,4,4,44,44,146,146,16,16,6,6,4,4,162

%N Least composite number m such that binomial(n+m,m) mod m = 1.

%H Harvey P. Dale, <a href="/A133905/b133905.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1)=4, since binomial(1+4,4) mod 4 = 5 mod 4 = 1 and 4 is the minimal composite number with this property.

%e a(5)=26 because of binomial(5+26,26)=169911=6535*26+1, but binomial(5+k,k) mod k<>1 for all composite numbers <26.

%t lcn[n_]:=Module[{m=4},While[PrimeQ[m]||Mod[Binomial[n+m,m],m]!=1,m++];m]; Array[lcn,80] (* _Harvey P. Dale_, May 13 2022 *)

%o (PARI) a(n) = { my(m = 4, ok = 0); until (ok, if (! isprime(m) && (binomial(n+m, m) % m == 1), ok = 1, m++);); return (m);} \\ _Michel Marcus_, Jul 15 2013

%Y Cf. A000040, A133620, A133621, A133623, A133630, A133635.

%Y Cf. A133872, A133880, A133890, A133900, A133910.

%K nonn

%O 1,1

%A _Hieronymus Fischer_, Oct 20 2007