A248854 Numbers n such that n - pi(n) is a power of 10.

1, 2, 3, 16, 17, 132, 1196, 11373, 110486, 1084604, 10708554, 106091744, 1053422338, 10475688326, 104287176418, 1039019056245, 10358018863852, 103307491450819, 1030734020030317, 10287026204717357, 102692313540015923, 1025351434864118025, 10239531292310798955, 102270102190290407385

Offset: 1

Author

Farideh Firoozbakht, Dec 31 2014

Keywords

• nonn
• hard

Comments

For n > 1 there exist at most two n-digit terms. If n is a term of the sequence and n + 1 is prime then n + 1 is also in the sequence.

Numbers n such that pi(n) is equal to n - 10^floor(log(10, n)). - Farideh Firoozbakht, Jan 01 2015

Crossrefs

Cf. A000720, A248856, A248857.

Programs

Maple

A[1]:= 1: A[2]:= 2: A[3]:= 3:
count:= 3:
for k from 1 to 8 do
  x:= 10^k; y:= x + numtheory:-pi(x);
  while x < y and y < 10^(k+1) do
    x:= y; y:= 10^k + numtheory:-pi(x);
  od;
  count:= count+1; A[count]:= x;
  if isprime(x+1) then
      count:= count+1; A[count]:= x+1
  fi;
od:
seq(A[i],i=1..count); # Robert Israel, Dec 31 2014

Mathematica

Select[Range[1000], IntegerQ[Log[10, # - PrimePi[#]]] &] (* Alonso del Arte, Jan 01 2015 *)

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(19)-a(24) from Giovanni Resta, Jun 07 2020