A091963 - OEIS

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

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OFFSET

2,1

COMMENTS

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

REFERENCES

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

LINKS

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

EXAMPLE

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.

MAPLE

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

PROG

(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

CROSSREFS

Cf. A014410.

Sequence in context: A356838 A079879 A071889 * A067695 A285336 A273282

Adjacent sequences: A091960 A091961 A091962 * A091964 A091965 A091966

KEYWORD

nonn

AUTHOR

David Wasserman, Mar 13 2004

STATUS

approved