A127181 a(1)=a(2)=1. a(n) = smallest possible (product of b(k)'s + product of c(k)'s), where the sequence's terms a(1) through a(n-1) are partitioned somehow into {b(k)} and {c(k)}.

1, 1, 2, 3, 5, 11, 37, 221, 3361, 190777, 83199527, 760382931109, 662056785094857629, 538451433632092674800570837, 12495147956629620251492228703104952798089, 1397663545252630798358314360015943050984074671707253231083973

Offset

1,3

Comments

Every term of the sequence is coprime to every other term.

Links

Max Alekseyev, Table of n, a(n) for n = 1..30

Example

By partitioning (a(1),a(2),...a(7)) = (1,1,2,3,5,11,37) into {b(k)} and {c(k)} so that {b(k)} = (1,2,5,11) and {c(k)} = (1,3,37), then (product of b(k)'s + product of c(k)'s) is minimized. Therefore a(8) = 1*2*5*11 + 1*3*37 = 221.

Mathematica

Nest[ Module[ {prod=Times@@#1}, Append[ #, Min[ #+prod/#&/@Times@@@Union[ Subsets[ # ] ] ] ] ]&, {1, 1, 2, 3}, 11 ] (Peter Pein (petsie(AT)dordos.net), Jan 07 2007)

Crossrefs

Cf. A127180.

Sequence in context: A006721 A111289 A255420 * A323611 A113734 A222007

Adjacent sequences: A127178 A127179 A127180 * A127182 A127183 A127184

Keyword

nonn

Author

Leroy Quet, Jan 07 2007

Extensions

a(10)-a(15) from Peter Pein (petsie(AT)dordos.net), Jan 07 2007

a(16)-a(30) from Max Alekseyev, Apr 08 2022

Status

approved