OFFSET
1,1
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)
LINKS
Harry J. Smith, Table of n, a(n) for n = 1..100
EXAMPLE
a(3) = prime(2) * prime(4) * prime(6) = 3 * 7 * 13 = 273.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Dec 16 2001
STATUS
approved