A095137 Absolute difference between the product of the first floor(n/2) even-indexed primes and the product of the first floor(n/2) odd-indexed primes.

2, 1, 7, 11, 89, 163, 1597, 3317, 37823, 107413, 1182887, 4232341, 49100059, 184657283, 2329965377, 10114830259, 138903895201, 622143222539, 9382665690241, 44778520855589, 686482057860331, 3598441529151191

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Formula

The absolute difference of Product_{j=1..floor(n/2)} p_(2j) (A066206) and Product_{k=1..floor(n/2)} p_(2j-1) (A066205).

Example

a(5) = 2*5*11 - 3*7 = 89, a(6) = 3*7*13 - 2*5*11 = 163;
a(7) = 2*5*11*17 - 3*7*13 = 1597, a(8) = 3*7*13*19 - 2*5*11*17 = 3317.

Mathematica

PrimeFactors[n_] := Flatten[ Table[ #[[1]], {1} ] & /@ FactorInteger[n]]; f[n_] := Abs[ Product[ Prime[i], {i, 2, n, 2}] + Product[ Prime[i], {i, 1, n, 2}]]; f[1] = 2; Table[ f[n], {n, 24}]
Join[{2}, Table[Abs[Times@@Prime[Range[1, Floor[n/2], 2]]-Times@@Prime[Range[ 2, Floor[ n/2 ], 2]]], {n, 4, 45, 2}]] (* Harvey P. Dale, Jan 11 2023 *)

Crossrefs

Cf. A095134, A000040, A066206, A066205.

Sequence in context: A100245 A275320 A272931 * A239104 A260259 A141488

Adjacent sequences: A095134 A095135 A095136 * A095138 A095139 A095140

Keyword

nonn

Author

Robert G. Wilson v, May 28 2004

Status

approved