Numbers n such that binomial(2n,n) is not divisible by 11, 13, 17, and 19.
0, 1, 2, 3, 4, 5, 57, 58, 364, 365, 408, 6942, 6943, 6944, 6955, 6956, 6957, 7282, 7283, 7284, 7296, 7297, 7298, 30761, 36179, 36180, 36181, 36182, 36183, 36184, 36195, 36234, 36235
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 infinite.
T. D. Noe, Plot of 33 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, 6], 11], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 7], 13], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 9], 17], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 10], 19], {k, 0, lim}]]
Cf. A151750 (the 3,5,7,11 case), S000720-S000724.
nonn,more
T. D. Noe, Oct 16 2015