A066206 a(n) = Product_{k=1..n} prime(2k), where prime(k) is the k-th prime.

3, 21, 273, 5187, 150423, 5565651, 239322993, 12684118629, 773731236369, 54934917782199, 4339858504793721, 386247406926641169, 39010988099590758069, 4174175726656211113383, 471681857112151855812279, 61790323281691893111408549, 8588854936155173142485788311

Offset: 1

Author

Leroy Quet, Dec 16 2001

Keywords

• nonn

Comments

From Jon E. Schoenfield, Jan 12 2022, Jan 15 2022: (Start)

Equivalently, a(n) is the product of the first n even-indexed primes.

Does r = prime(2n) * A066205(n)^2 / a(n)^2 approach a limit?

.

n A066205(n) a(n) prime(2n) r

---- -------------------- -------------------- ---------- ----------

1 2 3 3 1.33333...

10 10156396926610 54934917782199 71 2.42683...

100 4.93803636802*10^255 1.00181029905*10^257 1223 2.97141...

10^3 1.5455035248*10^3740 1.2239433562*10^3742 17389 2.77263...

10^4 1.760119173*10^48693 5.011593123*10^48695 224737 2.77208...

10^5 3.26453781*10^596726 3.25976132*10^596729 2750159 2.75822...

10^6 3.2925831*10^7045939 1.1297886*10^7045943 32452843 2.75633...

10^7 8.085113*10^81117222 9.413111*10^81117226 373587883 2.75612...

10^8 5.34067*10^916830347 2.09048*10^916830352 4222234741 2.75575...

(End)

Examples

			a(3) = prime(2) * prime(4) * prime(6) = 3 * 7 * 13 = 273.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A002110, A066205.

Programs

Maple

a:= proc(n) option remember;
     `if`(n=0, 1, a(n-1)*ithprime(2*n))
    end:
seq(a(n), n=1..17);  # Alois P. Heinz, Jan 12 2022

Mathematica

FoldList[Times, Prime@ Range[2, 30, 2]] (* Michael De Vlieger, Sep 24 2017 *)

PARI

{ for (n=1, 100, p=1; for (k=1, n, p*=prime(2*k)); write("b066206.txt", n, " ", p) ) } \\ Harry J. Smith, Feb 05 2010

PARI

a(n) = prod(k=1, n, prime(2*k)); \\ Michel Marcus, Jan 13 2022