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Numbers n such that 3 and 5 do not divide binomial(2n,n).
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%I #12 Feb 22 2022 09:53:59

%S 0,1,10,12,27,30,31,36,37,252,255,256,280,282,756,757,760,810,811,

%T 3160,3162,3186,3187,3250,3252,3276,3277,3280,6561,6562,6885,6886,

%U 6912,6925,7536,7537,7560,7561,7626,7627,7650,7651,19686,19687,20007,20010,20011

%N Numbers n such that 3 and 5 do not divide binomial(2n,n).

%C The Erdos paper proves that for any two odd primes p and q, there are an infinite number of n for which gcd(p*q,binomial(2n,n))=1; i.e., p and q do not divide binomial(2n,n).

%H T. D. Noe, <a href="/A129508/b129508.txt">Table of n, a(n) for n = 1..1000</a>

%H P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, <a href="https://users.renyi.hu/~p_erdos/1975-27.pdf">On the prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.

%F Intersection of A005836 and A037453.

%t lim=10000; Intersection[Table[FromDigits[IntegerDigits[k,2],3], {k,0,lim}], Table[FromDigits[IntegerDigits[k,3],5], {k,0,lim}]]

%o (PARI) valp(n, p)=my(s); while(n\=p, s+=n); s

%o is(n)=valp(2*n, 3)==2*valp(n, 3) && valp(2*n, 5)==2*valp(n, 5) \\ _Charles R Greathouse IV_, Feb 03 2016

%Y Cf. A030979 (n such that 3, 5 and 7 do not divide binomial(2n, n)).

%K nonn

%O 1,3

%A _T. D. Noe_, Apr 18 2007