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A066206
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a(n) = Product_{k=1..n} prime(2k), where prime(k) is the k-th prime.
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5
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3, 21, 273, 5187, 150423, 5565651, 239322993, 12684118629, 773731236369, 54934917782199, 4339858504793721, 386247406926641169, 39010988099590758069, 4174175726656211113383, 471681857112151855812279, 61790323281691893111408549, 8588854936155173142485788311
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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)
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LINKS
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Harry J. Smith, Table of n, a(n) for n = 1..100
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EXAMPLE
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a(3) = prime(2) * prime(4) * prime(6) = 3 * 7 * 13 = 273.
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MAPLE
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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
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MATHEMATICA
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FoldList[Times, Prime@ Range[2, 30, 2]] (* Michael De Vlieger, Sep 24 2017 *)
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PROG
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(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
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CROSSREFS
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Cf. A000040, A002110, A066205.
Sequence in context: A215127 A227820 A336809 * A130032 A174967 A126461
Adjacent sequences: A066203 A066204 A066205 * A066207 A066208 A066209
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet, Dec 16 2001
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STATUS
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approved
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