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

1,1

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).

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A010785, A105581.

Sequence in context: A341660 A033875 A105581 * A262363 A050264 A075239

Adjacent sequences: A258430 A258431 A258432 * A258434 A258435 A258436

Keyword

nonn,base

Author

James G. Merickel, May 29 2015

Status

approved