A091963 a(n) is the smallest gcd of two interior numbers on row n of Pascal's triangle ("interior" means that the 1's at the ends of the rows are excluded).

2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 3, 13, 2, 3, 2, 17, 2, 19, 4, 3, 2, 23, 3, 5, 2, 3, 4, 29, 6, 31, 2, 3, 2, 5, 4, 37, 2, 3, 5, 41, 6, 43, 4, 3, 2, 47, 3, 7, 2, 3, 4, 53, 2, 5, 7, 3, 2, 59, 4, 61, 2, 7, 2, 5, 6, 67, 4, 3, 10, 71, 4, 73, 2, 3, 4, 7, 2, 79, 5, 3, 2, 83, 12, 5, 2, 3, 4, 89, 9, 7, 4, 3, 2, 5, 3

Offset: 2

Author

David Wasserman, Mar 13 2004

Keywords

• nonn

Comments

The reference contains a simple proof that there are no 1's in this sequence.

Examples

			In row 8, the interior numbers 8, 28, 56 and 70; gcd(8, 28) = 4; gcd(8, 56) = 8; gcd(8, 70) = 2; gcd(28, 56) = 28; gcd(28, 70) = 14; gcd(56, 70) = 14. The smallest of these is 2, so a(8) = 2.
		

References

• R. K. Guy, Unsolved Problems in Number Theory, Sections B31, B33.

Links

• Robert Israel, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A014410.

Programs

Maple

seq(min(seq(igcd(n,binomial(n,k)),k=1..floor(n/2))), n=2..100); # Robert Israel, Jun 17 2014

PARI

a(n) = {v = vector(n\2, i, binomial(n, i)); mgcd = n; for (i=1, #v, for (j=i+1, #v, mgcd = min(gcd(v[i], v[j]), mgcd););); return (mgcd);} \\ Michel Marcus, Jun 16 2013