Search: id:A030979
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%I A030979
%S A030979 0,1,10,756,757,3160,3186,3187,3250,7560,7561,7651,20007,59548377,
%T A030979 59548401,45773612811,45775397187,237617431723407,24991943420078301,
%U A030979 24991943420078302,24991943420078307,24991943715007536,24991943715007537
%N A030979 Numbers n such that C(2n,n) is not divisible by 3, 5 or 7.
%C A030979 By Lucas' theorem, C(2n,n) is not divisible by a prime p iff all base-p 
               digits of n are smaller than p/2.
%C A030979 Ronald L. Graham (graham(AT)ucsd.edu) offers $1000 to the first person 
               who can settle the question of whether this sequence is finite or 
               infinite. He remarks that heuristic arguments show that it should 
               be infinite, but finite if it is required that C(2n,n) is prime to 
               3, 5, 7 and 11, with n = 3160 probably the last n which has this 
               property.
%C A030979 The Erdos et al. paper shows 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). The paper does not deal 
               with the case of three primes. - T. D. Noe (noe(AT)sspectra.com), 
               Apr 18 2007
%D A030979 Mauldin, R. Daniel; Ulam, S. M.; Mathematical problems and games. Adv. 
               in Appl. Math. 8 (1987), 281-344. [From N. J. A. Sloane, Jul 30 2009]
%H A030979 Max Alekseyev <a href="b030979.txt">Values of a(n) for n=1..62</a> (complete 
               up to 3^41)
%H A030979 P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, <a href="http:/
               /www.math.ucsd.edu/%7Esbutler/ron/75_03_prime_factors.pdf">On the 
               prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.
%H A030979 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucas%27_theorem">Lucas' 
               theorem</a>
%F A030979 Intersection of A005836, A037453 and A037461. - T. D. Noe (noe(AT)sspectra.com), 
               Apr 18 2007
%t A030979 lim=10000; Intersection[Table[FromDigits[IntegerDigits[k,2],3], {k,0,
               lim}], Table[FromDigits[IntegerDigits[k,3],5], {k,0,lim}], Table[FromDigits[IntegerDigits[k,
               4],7], {k,0,lim}]] - T. D. Noe (noe(AT)sspectra.com), Apr 18 2007
%Y A030979 Cf. A129488, A129489, A129508, A151750.
%Y A030979 Sequence in context: A008272 A015509 A117257 this_sequence A108247 A108243 
               A159709
%Y A030979 Adjacent sequences: A030976 A030977 A030978 this_sequence A030980 A030981 
               A030982
%K A030979 nonn
%O A030979 1,3
%A A030979 Shawn Godin (sgodin(AT)onlink.net)
%E A030979 More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), May 06 2002
%E A030979 Additional comments from Ron Graham, Apr 25 2007
%E A030979 Additional comments and terms up 3^41 in b-file from Max Alekseyev (maxale(AT)gmail.com), 
               Nov 23 2008

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