A129508 Numbers n such that 3 and 5 do not divide binomial(2n,n).

0, 1, 10, 12, 27, 30, 31, 36, 37, 252, 255, 256, 280, 282, 756, 757, 760, 810, 811, 3160, 3162, 3186, 3187, 3250, 3252, 3276, 3277, 3280, 6561, 6562, 6885, 6886, 6912, 6925, 7536, 7537, 7560, 7561, 7626, 7627, 7650, 7651, 19686, 19687, 20007, 20010, 20011

Offset

1,3

Comments

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).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, On the prime factors of C(2n,n), Math. Comp. 29 (1975), 83-92.

Formula

Intersection of A005836 and A037453.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A108901 A372488 A073083 * A015728 A080470 A087217

Adjacent sequences: A129505 A129506 A129507 * A129509 A129510 A129511

Keyword

nonn

Author

T. D. Noe, Apr 18 2007

Status

approved