A173501 - OEIS

A173501

a(1) = 2, a(2) = 3, a(n) = 6^(2^(n-3)) for n >= 3.

2, 3, 6, 36, 1296, 1679616, 2821109907456, 7958661109946400884391936, 63340286662973277706162286946811886609896461828096

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OFFSET

1,1

COMMENTS

Except for first three terms, a(n) = (a(n-1))^2.

Essentially the same as A165424. - R. J. Mathar, Feb 21 2010

LINKS

FORMULA

a(n) = Product_{i=1..n-1} a(i) with a(1) = 2 and a(2) = 3.

a(n) = 6^(2^(n-3)) = A000400(A000079(n-3)) for n>2.

From Amiram Eldar, Nov 30 2025: (Start)

Sum_{n>=1} 1/a(n) = 5/6 + A078887.

Product_{n>=1} (1 + 1/a(n)) = 12/5. (End)

MATHEMATICA

Table[If[n<3, n+1, 6^(2^(n-3))], {n, 10}] (* G. C. Greubel, Apr 25 2021 *)

PROG

(SageMath) [2, 3]+[6^(2^(n-3)) for n in (3..10)] # G. C. Greubel, Apr 25 2021

(PARI) a(n) = if(n<=2, n+1, 6^(2^(n-3))) \\ Felix Fröhlich, Apr 25 2021

CROSSREFS

KEYWORD

nonn

AUTHOR

EXTENSIONS

Definition corrected by Glenn Tesler, Aug 19 2017

STATUS

approved