A095134 - OEIS

%I #18 Dec 03 2024 12:25:33

%S 2,5,13,31,131,383,2143,7057,48197,193433,1483733,6898961,60231361,

%T 293988703,2808611363,15253406999,164272132459,925319250199,

%U 10930128162979,65091314708809,796351893424729,5081275480436251

%N Sum of the product of the first ceiling(n/2) odd-indexed primes and the product of the first floor(n/2) even-indexed primes; a(1) = 2.

%H Robert Israel, <a href="/A095134/b095134.txt">Table of n, a(n) for n = 1..631</a>

%F Sum_{i=1..n} of the product_{j=2..n, 2} p_j (A066206) and the product_{k=1..n, 2} p_j (A066205).

%e a(5) = 2*5*11 + 3*7 = 131, a(6) = 2*5*11 + 3*7*13 = 383;

%e a(7) = 2*5*11*17 + 3*7*13 = 2143, a(8) = 2*5*11*17 + 3*7*13*19 = 7057.

%p p:= 2: R:= 2: a:= 2: b:= 1:

%p for m from 1 to 10 do

%p   p:= nextprime(p); b:= b*p; R:= R,a+b;

%p   p:= nextprime(p); a:= a*p; R:= R,a+b;

%p od:

%p R; # _Robert Israel_, Dec 01 2024

%t f[n_] := Product[Prime[i], {i, 2, n, 2}] + Product[Prime[i], {i, 1, n, 2}]; f[1] = 2; Table[ f[n], {n, 22}]

%o (PARI) a(n) = if (n==1, 2, vecprod(vector(floor(n/2), k, prime(2*k)))+vecprod(vector(ceil(n/2), k, prime(2*k-1)))); \\ _Michel Marcus_, Dec 03 2024

%Y Cf. A095137, A000040, A066206, A066205.

%K nonn

%O 1,1

%A _Robert G. Wilson v_, May 27 2004