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

1,2

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

Links

Table of n, a(n) for n=1..24.

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 *)

Prog

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

Crossrefs

Cf. A000720, A248856, A248857.

Sequence in context: A076801 A032807 A246490 * A167605 A043308 A061918

Adjacent sequences: A248851 A248852 A248853 * A248855 A248856 A248857

Keyword

nonn,hard

Author

Farideh Firoozbakht, Dec 31 2014

Extensions

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

Status

approved