A100042 a(n) = prime(n)*2^prime(n).

8, 24, 160, 896, 22528, 106496, 2228224, 9961472, 192937984, 15569256448, 66571993088, 5085241278464, 90159953477632, 378231999954944, 6614661952700416, 477381560501272576, 34011184385901985792

Offset: 1

Author

Jorge Coveiro, Dec 26 2004

Keywords

• nonn

Comments

A lower bound for the 2-color van der Waerden number A005346(prime(n)); see Berlekamp reference. - Charles R Greathouse IV, Jul 13 2008

Links

• E. R. Berlekamp, A construction for partitions which avoid long arithmetic progressions, Canadian Mathematical Bulletin, Vol. 11, No. 3 (1968), pp. 409-414.

Crossrefs

Cf. A005346, A034785, A157413.

Programs

Maple

seq(ithprime(n)*2^ithprime(n),n=1..20);

Mathematica

#*2^#&/@Prime[Range[20]] (* Harvey P. Dale, Sep 18 2020 *)

PARI

a(n) = prime(n)*2^prime(n); \\ Michel Marcus, May 14 2017

Formula

Sum_{n>=1} 1/a(n) = A157413. - Amiram Eldar, Nov 17 2020