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A133908

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

3, 3, 5, 5, 7, 7, 11, 11, 3, 3, 3, 13, 17, 17, 17, 17, 19, 3, 3, 3, 23, 23, 29, 29, 5, 5, 3, 3, 3, 31, 37, 37, 37, 37, 37, 3, 3, 3, 41, 41, 43, 43, 47, 47, 3, 3, 3, 53, 7, 5, 5, 5, 5, 3, 3, 3, 59, 59, 61, 61, 67, 67, 3, 3, 3, 67, 71, 71, 71, 71, 73, 3, 3, 3, 5, 5, 5, 5, 5, 83, 3, 3, 3, 89, 89

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OFFSET

1,1

COMMENTS

Also the least odd prime number m such that m divides floor(n/m) or m>n.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

a(3)=5, since binomial(3+5,5) mod 5 = 56 mod 5 = 1 and 5 is the minimal odd prime number with this property.

a(8)=11 because of binomial(8+11,11)=75582=6871*11+1, but binomial(8+k,k) mod k<>1 for all odd primes <11.

MATHEMATICA

With[{oprs=Rest[Prime[Range[100]]]}, Flatten[Table[Select[oprs, Mod[ Binomial[ n+#, #], #]==1&, 1], {n, 90}]]] (* Harvey P. Dale, Jun 27 2012 *)