A095134 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.

2, 5, 13, 31, 131, 383, 2143, 7057, 48197, 193433, 1483733, 6898961, 60231361, 293988703, 2808611363, 15253406999, 164272132459, 925319250199, 10930128162979, 65091314708809, 796351893424729, 5081275480436251

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..631

Formula

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

Example

a(5) = 2*5*11 + 3*7 = 131, a(6) = 2*5*11 + 3*7*13 = 383;
a(7) = 2*5*11*17 + 3*7*13 = 2143, a(8) = 2*5*11*17 + 3*7*13*19 = 7057.

Maple

p:= 2: R:= 2: a:= 2: b:= 1:
for m from 1 to 10 do
  p:= nextprime(p); b:= b*p; R:= R, a+b;
  p:= nextprime(p); a:= a*p; R:= R, a+b;
od:
R; # Robert Israel, Dec 01 2024

Mathematica

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

Prog

(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

Crossrefs

Cf. A095137, A000040, A066206, A066205.

Sequence in context: A056367 A378111 A082733 * A086758 A179257 A116702

Adjacent sequences: A095131 A095132 A095133 * A095135 A095136 A095137

Keyword

nonn

Author

Robert G. Wilson v, May 27 2004

Status

approved