A132181 a(n)=smallest positive integer such that product{k=1 to n}(1+1/a(k)) has a prime numerator.

1, 2, 6, 1, 28, 1, 1, 58, 1, 708, 1, 1, 2, 1, 2836, 1, 1, 22696, 1, 1, 1, 590122, 1, 12, 1, 1, 2, 1, 1180246, 1, 9441976, 1, 1, 1, 169955586, 1, 2, 1, 2, 1, 2719289392, 1, 1, 1, 1, 5438578786, 1, 32631472722, 1, 2, 1, 391577672676, 1, 1, 2, 1, 1566310690708, 1, 1

Offset

1,2

Links

Owen Whitby, Table of n, a(n) for n = 1..200

Formula

Comments from Owen Whitby, May 07 2008 (Start): Successive terms a(.) can be calculated using the following recurrences for the numerator n(.) and denominator d(.) of the product.

a(1)=1; n(1)=1, d(1)=1 ==> a(2)=1, n(2)=2, d(2)=1 ( to start things off );

n(i)=2, d(i)= odd ==> a(i+1)=q-1, n(i+1)=q, d(i+1)=d(i)(q-1)/2 where q is least odd prime not dividing d(i);

n(i)=odd prime, d(i)=1 ==> a(i+1)=c*n(i), n(i+1)=c*n(i)+1, d(i+1)=c where c is least even integer such that c*n(i)+1 is prime;

n(i)=odd prime, d(i)=even ==> a(i+1)=1, n(i+1)=n(i), d(i+1)=d(i)/2;

n(i)=odd prime, d(i)= odd>=3 ==> a(i+1)=p-1, n(i+1)=n(i), d(i+1)=d(i)(p-1)/p where p is least prime divisor of d(i). (End)

Crossrefs

Sequence in context: A281521 A281635 A180512 * A364374 A291646 A366152

Adjacent sequences: A132178 A132179 A132180 * A132182 A132183 A132184

Keyword

nonn

Author

Leroy Quet, Nov 04 2007

Extensions

a(10) to a(59) and list of 200 terms added by Owen Whitby, May 07 2008

Status

approved