A171645 Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes, A000040, a(1) = 2.

2, 4, 8, 12, 18, 30, 50, 70, 98, 154, 242, 286, 338, 442, 578, 646, 722, 874, 1058, 1334, 1682, 1798, 1922, 2294, 2738

Offset

1,1

Comments

Analogous formulas using A000041 terms = A171646; Fibonacci numbers, A006498; factorials, A010551.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Partial products of Product_{n=1..inf.} (p(n)/p(n-1)*p(n)/p(n-1)), =

2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7)*(11/7)*...; p = primes,

A000040, a(1) = 2.

a(n)=2*A057602(n-1). [From R. J. Mathar, Dec 15 2009]

Example

a(10) = 154 = 2*2*2*(3/2)*(3/2)*(5/3)*(5/3)*(7/5)*(7/5)*(11/7).

Mathematica

FoldList[Times, Join[{2, 2, 2}, Flatten[{#[[2]]/#[[1]], #[[2]]/#[[1]]}&/@Partition[Prime[Range[20]], 2, 1]]]] (* Harvey P. Dale, Oct 02 2024 *)

Crossrefs

Cf. A171646, A006498, A010551.

Sequence in context: A294049 A006500 A134181 * A125606 A192078 A136184

Adjacent sequences: A171642 A171643 A171644 * A171646 A171647 A171648

Keyword

nonn

Author

Gary W. Adamson, Dec 13 2009

Status

approved