A258433 Primes with repdigit indices (in decimal).

2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 79, 137, 193, 257, 317, 389, 457, 523, 607, 1399, 2239, 3119, 4019, 4973, 5903, 6907, 7907, 8933, 19583, 30911, 42473, 54581, 66889, 79357, 92003, 104723, 117763, 252233, 393191, 538259, 686671, 836833, 989999, 1144153, 1299689, 1456667, 3080969, 4767181, 6495109, 8251153

Offset: 1

Author

James G. Merickel, May 29 2015

Keywords

• nonn
• base

Comments

Elements of this sequence are the first 9 primes, then the 11th, 22nd, 33rd, ... , 99th, 111th, 222nd, etc. This is a somewhat remarkable sequence because of certain digital coincidences (see Prime Curios links).

Examples

			The first prime skipped is the 10th, 29, so that a(10)=31.  Then follows a(11)=79, a(12)=137, a(13)=193, etc.: The 22nd, 33rd, and 44th primes, and so on.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..153
• Andrew Booker, The Nth Prime Page
• Prime Curios!, 989999
• Prime Curios!, 640663963
• Wikipedia, Repdigit
• Wikipedia, Prime-counting function

Crossrefs

Cf. A000040, A010785, A105581.

Programs

Mathematica

Prime[#]&/@(FromDigits/@Flatten[Table[PadRight[{},k,n],{k,6},{n,9}],1]) (* Harvey P. Dale, Mar 25 2019 *)

PARI

a(n)=prime(10^((n+8)\9)\9*((n-1)%9+1)) \\ Charles R Greathouse IV, Jun 03 2015

Formula

a(n) = A000040(A010785(n)).