A244085 - OEIS

A244085

Primes p such that the concatenation of p and 2*p-1 is also prime.

2, 5, 17, 29, 47, 61, 137, 149, 179, 181, 227, 251, 349, 367, 409, 457, 461, 479, 487, 557, 569, 617, 661, 691, 761, 787, 809, 821, 859, 911, 971, 977, 997, 1039, 1117, 1129, 1151, 1249, 1277, 1367, 1439, 1447, 1459, 1481, 1559, 1571, 1667, 1747, 1801, 1831

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The corresponding prime numbers are: (23, 59, 1733, 2957, 4793, 61121, ...).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

EXAMPLE

17 in this sequence because the concatenation of 17 and 33 is 1733 prime.

MATHEMATICA

p2pQ[n_]:=PrimeQ[FromDigits[IntegerDigits/@Join[n, 2 n - 1]]]; Select[Prime[Range[900]], p2pQ]

Select[Prime[Range[900]], With[{c=2#-1}, PrimeQ[#*10^IntegerLength[c]+c]]&] (* Harvey P. Dale, Feb 06 2025 *)