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%I #29 May 27 2018 01:39:01
%S 1,853,91182,926756,9374193,94535668,951496285,9563906973,
%T 963706466000,9665127969899,96891533076641,970995550452370,
%U 9728143518403637,97441817594570206,975843062833251485,9771174122943813068
%N Numbers n such that n + pi(n) is a power of 10.
%C Numbers n such that pi(n) equals 10^ceiling(log(10,n)) - n.
%C 853 is the only known prime term of the sequence. If n is a prime term of the sequence and m = pi(n) then prime(m) + m is a power of 10. So 147 = pi(853) is the only known number m such that prime(m) + m is a power of 10. What is the next such number?
%C For each number n there exists at most one n-digit term.
%C a(11) = 96891533076641 is also prime. - _Chai Wah Wu_, May 25 2018
%e pi(96891533076641) + 96891533076641 = 10^14 so 96891533076641 is in the sequence.
%t Select[Range[1000], IntegerQ[Log[10, # + PrimePi[#]]] &] (* _Alonso del Arte_, Dec 31 2014 *)
%o (PARI) for(n=1,10^3,s=digits(n+primepi(n)-1);if(s==[]||vecmin(s)==9,print1(n,", "))) \\ _Derek Orr_, Jan 02 2015
%Y Cf. A000720, A244440, A248854.
%K nonn,hard
%O 1,2
%A _Farideh Firoozbakht_, Dec 31 2014
%E a(12)-a(16) from _Chai Wah Wu_, May 25 2018
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