A306572 Numbers k whose decimal representation ends with that of pi(k) (where pi denotes the prime counting function A000720).

16, 17, 132, 254, 374, 494, 1196, 2348, 3487, 4624, 5757, 6886, 11373, 22517, 33597, 44639, 55646, 66644, 77629, 88580, 99550, 99551, 110486, 219572, 328268, 436699, 544946, 653052, 761059, 869024, 976855, 1084604, 1192399, 2159962, 3232398, 4303026, 4303027

Offset: 1

Author

Rémy Sigrist, Feb 24 2019

Keywords

• nonn
• base

Comments

This sequence contains the automorphic primes (A046883).

If p is an automorphic prime, then p-1 is a term of the sequence.

Examples

			There are 7 prime numbers <= 17, and 17 ends with 7, hence 17 is a term.
There are 13 prime numbers <= 42, and 42 does not end with 13, hence 42 is not a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..310

Crossrefs

Cf. A000720, A046883, A067248.

Programs

Mathematica

Select[Range[2, 10^6], Mod[#1, 10^(1 + Floor@ Log10[#2])] == #2 & @@ {#, PrimePi@ #} &] (* Michael De Vlieger, Apr 06 2021 *)

PARI

pi=0; for (n=1, 4303027, if (n%10^max(1,#digits(pi+=isprime(n)))==pi, print1 (n ", ")))

Python

from sympy import primepi
A306572_list = [n for n, p in enumerate(primepi(k) for k in range(10**4)) if n > 0 and n % 10**len(str(p)) == p] # Chai Wah Wu, Apr 06 2021