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Numbers n such that pi(n) = P(d_1!!)*P(d_2!!)*...*P(d_k!!) where d_1 d_2 ... d_k is the decimal expansion of n and P(i) is i-th prime.
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%I #21 Mar 06 2019 14:30:50

%S 10,30,123,41402,1400523,3173000,3173001,3173010,3173011,351226103,

%T 351226113,351226130,351226131

%N Numbers n such that pi(n) = P(d_1!!)*P(d_2!!)*...*P(d_k!!) where d_1 d_2 ... d_k is the decimal expansion of n and P(i) is i-th prime.

%C There are no further terms up to 35000000.

%C From _Farideh Firoozbakht_, Jun 01 2009: (Start)

%C If 10*n is in the sequence and 10*n+1 is composite then 10*n+1 is also in the sequence.

%C There is no further term up to 1.5*10^10. (End)

%C There are no other terms less than 10^15. - _Chai Wah Wu_, Mar 06 2019

%e 3173011 is in the sequence because pi(3173011)=P(3!!)*P(1!!)*P(7!!)*P(0!!)*P(1!!)*P(1!!).

%t Do[d=IntegerDigits[n];k=Length[d];If[PrimePi[n]== Product[Prime[d[[j]]!! ], {j, k}], Print[n]], {n, 35000000}]

%Y Cf. A000040, A098683, A098685, A098686.

%K base,more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Sep 24 2004

%E More terms from _Farideh Firoozbakht_, Jun 01 2009