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%I #31 May 17 2020 17:47:29
%S 1,1,3,6,2,1,1,35,15,3,2,1,3,5,14,6,6,7,1,1,5,4,4,15,3,1,2,2,55,5,4,3,
%T 1,1,3,84,1,1,28,10,3,3,1,1,1,221,3,6,2,7,3,15,231,21,7,1,5,70,3,1,
%U 1292,35,1,3,15,24,7,1,6,7,1,3,42,5,1,231,35,1,143,2,5,1,1,7,14,1,45,3
%N Greatest common divisor of two binomial coefficients formed from consecutive primes: a(n) = gcd(C(prime(n+2), prime(n+1)), C(prime(n+1), prime(n))).
%H Robert Israel, <a href="/A058078/b058078.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = gcd(f(n+1), f(n)) where f(n) = binomial(prime(n+1), prime(n)). - _Joerg Arndt_, Apr 05 2014
%e n = 8, a(8) = gcd(C(prime(10), prime(9)), C(prime(9), prime(8))) = gcd(C(29, 23), C(23, 19)) = gcd(8855, 475020) = gcd(5*7*11*23, 2^2*3^2*5*7*13*29) = 5*7 = 35.
%p A058078:=n->gcd(binomial(ithprime(n+2),ithprime(n+1)), binomial(ithprime(n+1), ithprime(n))); seq(A058078(n), n=1..100); # _Wesley Ivan Hurt_, Apr 01 2014
%t GCD[Binomial[Last[#],#[[2]]],Binomial[#[[2]],First[#]]]&/@ Partition[ Prime[ Range[90]],3,1] (* _Harvey P. Dale_, May 05 2011 *)
%o (PARI) a(n,p=prime(n))=my(q=nextprime(p+1),r=nextprime(q+1)); gcd(binomial(r,q), binomial(q,p)) \\ _Charles R Greathouse IV_, Nov 18 2015
%Y Cf. A058077, A334906.
%K nonn
%O 1,3
%A _Labos Elemer_, Nov 13 2000
%E Edited by _Wolfdieter Lang_, Apr 16 2014
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