A248856 Numbers n such that n + pi(n) is a power of 10.

1, 853, 91182, 926756, 9374193, 94535668, 951496285, 9563906973, 963706466000, 9665127969899, 96891533076641, 970995550452370, 9728143518403637, 97441817594570206, 975843062833251485, 9771174122943813068

Offset: 1

Author

Farideh Firoozbakht, Dec 31 2014

Keywords

• nonn
• hard

Comments

Numbers n such that pi(n) equals 10^ceiling(log(10,n)) - n.

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?

For each number n there exists at most one n-digit term.

a(11) = 96891533076641 is also prime. - Chai Wah Wu, May 25 2018

Examples

			pi(96891533076641) + 96891533076641 = 10^14 so 96891533076641 is in the sequence.
		

Crossrefs

Cf. A000720, A244440, A248854.

Programs

Mathematica

Select[Range[1000], IntegerQ[Log[10, # + PrimePi[#]]] &] (* Alonso del Arte, Dec 31 2014 *)

PARI

for(n=1,10^3,s=digits(n+primepi(n)-1);if(s==[]||vecmin(s)==9,print1(n,", "))) \\ Derek Orr, Jan 02 2015

Extensions

a(12)-a(16) from Chai Wah Wu, May 25 2018