A058078 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))).

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, 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, 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

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = gcd(f(n+1), f(n)) where f(n) = binomial(prime(n+1), prime(n)). - Joerg Arndt, Apr 05 2014

Example

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.

Maple

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

Mathematica

GCD[Binomial[Last[#], #[[2]]], Binomial[#[[2]], First[#]]]&/@ Partition[ Prime[ Range[90]], 3, 1] (* Harvey P. Dale, May 05 2011 *)

Prog

(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

Crossrefs

Cf. A058077, A334906.

Sequence in context: A332505 A303864 A058178 * A016551 A238555 A176034

Adjacent sequences: A058075 A058076 A058077 * A058079 A058080 A058081

Keyword

nonn

Author

Labos Elemer, Nov 13 2000

Extensions

Edited by Wolfdieter Lang, Apr 16 2014

Status

approved