A171645 - OEIS

%I #8 Oct 02 2024 19:21:35

%S 2,4,8,12,18,30,50,70,98,154,242,286,338,442,578,646,722,874,1058,

%T 1334,1682,1798,1922,2294,2738

%N 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.

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

%H Harvey P. Dale, <a href="/A171645/b171645.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%F A000040, a(1) = 2.

%F a(n)=2*A057602(n-1). [From _R. J. Mathar_, Dec 15 2009]

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

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

%Y Cf. A171646, A006498, A010551.

%K nonn,changed

%O 1,1

%A _Gary W. Adamson_, Dec 13 2009