Numbers n such that binomial(2n,n) is not divisible by 5, 7, 11, and 13.
0, 1, 2, 56, 57, 176310, 176311, 176312
1
The sequence for the 3-5-7-11 case has only 3 terms. These related five sequences (S000720-S000724) provide more insight to the problem. Using the analysis of the Pomerance paper, this sequence is expected to be finite.
T. D. Noe, Plot of 8 terms
Carl Pomerance, Divisors of the middle binomial coefficient, Amer. Math. Monthly, 122 (2015), pp. 636-644.
(Mma) lim = 1000000; Intersection[Table[FromDigits[IntegerDigits[k, 3], 5], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 4], 7], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 6], 11], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 7], 13], {k, 0, lim}]]
Cf. A151750 (the 3,5,7,11 case), S000721-S000724.
nonn,more
T. D. Noe, Oct 16 2015