A127166 a(n) = the minimum prime S possible, if S = product of b(k)'s + product of c(k)'s, where the distinct positive integers <= n are partitioned into the two sets {b(k)} and {c(k)}. a(n) = 0 if no prime S exists for that n.

2, 2, 3, 5, 11, 23, 149, 179, 1187, 0, 0, 3628811, 43545611, 43545743, 7925299211, 9144576143, 1609445376013, 32335220736011, 44771844096143, 582033973248209, 52672757806189, 18804174520322717, 267682954936324199

Offset

0,1

Comments

a(0)=a(1)=2 because the product over the empty set is defined here as 1. For S to be a prime, the positive integers <= n, except 1 and the primes > n/2, must all be together in either {b(k)} or {c(k)}. If p is a prime where n/2 < p <= n, then it is possible that p is in either product of the S sum, as can 1. Terms calculated by W. Edwin Clark.

Links

Ray Chandler, Table of n, a(n) for n=0..100

Example

For n = 6 we have the only prime S (and so the minimum prime S) with S = 1*2*3*4*6 + 5 = 149.

Mathematica

f[n_] := Block[{d = Divisors[Times @@ Select[Range[n], PrimeQ[ # ] && 2# > n &]]}, Select[Union[d + n!/d], PrimeQ]]; If[ # == {}, 0, First[ # ]] & /@ Array[f, 30, 0] (* Ray Chandler, Feb 14 2007 *)

Crossrefs

Cf. A127165, A128199.

Sequence in context: A030427 A049907 A078445 * A103596 A005426 A014644

Adjacent sequences: A127163 A127164 A127165 * A127167 A127168 A127169

Keyword

nonn

Author

Leroy Quet, Jan 06 2007

Extensions

a(21)-a(35) from Ray Chandler, Feb 14 2007

Status

approved