A155032 Primes p such that both pi(p) and the concatenation of pi(p) and p are prime, where pi is the prime counting function.

3, 59, 83, 179, 283, 353, 431, 709, 1433, 2269, 2381, 3559, 3593, 4153, 5503, 6899, 7109, 7351, 7649, 8513, 11909, 13297, 14107, 14437, 14591, 16073, 16127, 16451, 16901, 17117, 17539, 17987, 18149, 19777, 20759, 21317, 22027, 24439, 25357, 26783, 27437, 29269, 30253, 32299, 34057, 34259, 34421, 34543, 35617, 36307, 37049

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

Since 3 is the second prime number and the concatenation of 2 and 3 gives 23, which is prime, 3 is in the sequence.
Since 59 is the seventeenth prime and the concatenation of 17 and 59 gives 1759, another prime, 59 is also in the sequence.

Mathematica

(* First run the program given for A154963 *) Prime[A154963]
Module[{nn=1000}, Select[Table[{n, Prime[n]}, {n, Prime[Range[nn]]}], PrimeQ[#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]]&]][[;; , 2]] (* Harvey P. Dale, Jul 20 2025 *)

Crossrefs

pi(a(n)) = A154963(n).

Sequence in context: A139882 A385851 A139874 * A107212 A002148 A290977

Adjacent sequences: A155029 A155030 A155031 * A155033 A155034 A155035

Keyword

nonn,base

Author

Juri-Stepan Gerasimov, Jan 19 2009

Extensions

Edited and extended beyond a(3) by Alonso del Arte, Jan 20 2009, with thanks to Klaus Brockhaus's edit of A154963

Name clarified by Sean A. Irvine, Jul 20 2025

Status

approved