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Partial products of successive digits in the decimal expansion of Pi.
3

%I #13 Dec 15 2020 12:48:48

%S 3,3,12,12,60,540,1080,6480,32400,97200,486000,3888000,34992000,

%T 244944000,2204496000,6613488000,13226976000,39680928000,317447424000,

%U 1269789696000,7618738176000,15237476352000,91424858112000

%N Partial products of successive digits in the decimal expansion of Pi.

%C Because 33rd digit in the decimal expansion of Pi, pi(33) = 0, all a(n>32) = 0.

%C Partial sums of digits of the decimal expansion of Pi are in A046974.

%F a(n) = pi(1)*...*pi(n); pi(n)=A000796(n).

%F a(n) = A073055(n), n>0. - _R. J. Mathar_, Dec 15 2020

%e a(3)=12 because pi(1)=3, pi(1)=1, pi(3)=4 and a(3)=3*1*4=12.

%t ppi={3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, 2, 8}; Table[Product[ppi[[i]], {i, n}], {n, 1, 33}]

%t Rest[FoldList[Times,1,RealDigits[Pi,10,30][[1]]]] (* _Harvey P. Dale_, Jan 23 2015 *)

%Y Cf. A000796, A046974, A073055.

%K nonn,base

%O 1,1

%A _Zak Seidov_, Sep 10 2002