Numbers n such that binomial(2n,n) is not divisible by 17, 19, 23, and 29.
0, 1, 2, 3, 4, 5, 6, 7, 8, 119, 120, 121, 122, 123, 1160, 1161, 1197, 1198, 1224, 1225, 1805, 1827, 30345, 30346, 30347, 30348, 30363, 30364, 30365, 30366, 30367, 30368, 30369, 30370, 36524, 3129683, 3129684, 3129685, 3129686, 3129687, 3129688, 3129689, 3130231
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 263 terms
T. D. Noe, Table of 263 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, 9], 17], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 10], 19], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 12], 23], {k, 0, lim}], Table[FromDigits[IntegerDigits[k, 15], 29], {k, 0, lim}]]
Cf. A151750 (the 3,5,7,11 case), S000720-S000723.
nonn
T. D. Noe, Oct 16 2015