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A129508 Numbers n such that 3 and 5 do not divide binomial(2n,n). 6
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 (list; graph; refs; listen; history; text; internal format)
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: A140972 A108901 A073083 * A015728 A080470 A087217

Adjacent sequences:  A129505 A129506 A129507 * A129509 A129510 A129511

KEYWORD

nonn

AUTHOR

T. D. Noe, Apr 18 2007

STATUS

approved

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Last modified November 21 13:53 EST 2017. Contains 295001 sequences.