A034808 Concatenation of 'prevprime(n) and n' is a prime.

3, 9, 37, 39, 51, 63, 87, 89, 111, 117, 123, 153, 157, 163, 173, 177, 183, 207, 211, 213, 217, 219, 239, 249, 257, 263, 267, 269, 273, 277, 279, 289, 321, 323, 327, 333, 337, 339, 343, 359, 369, 379, 407, 423, 439, 441, 459, 471, 473, 477, 479, 489, 497, 513

Offset

0,1

Comments

Since there are primes in the sequence, and concat(p,p) = p*(10^x+1) is always composite, it is clear that here the variant 2 (A151799(n) < n) of the prevprime function is used, rather than the variant 1 (A007917(n) <= n). - M. F. Hasler, Sep 09 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

n=333 -> previous prime is 331, thus '331333' is a prime.

Mathematica

coQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits[{NextPrime[n, -1], n}]]]]; Select[Range[3, 513], coQ[#]&] (* Jayanta Basu, May 30 2013 *)
Select[Range[2, 550], PrimeQ[NextPrime[#, -1]*10^IntegerLength[#]+#]&] (* Harvey P. Dale, Nov 22 2020 *)

Prog

(Python)
from sympy import isprime, prevprime
def aupto(m):
  return [k for k in range(3, m+1) if isprime(int(str(prevprime(k))+str(k)))]
print(aupto(513)) # Michael S. Branicky, Mar 09 2021

Crossrefs

Cf. A034809-A034821.

Cf. A151799, A007917.

Sequence in context: A135474 A279121 A076964 * A018398 A197309 A149021

Adjacent sequences: A034805 A034806 A034807 * A034809 A034810 A034811

Keyword

nonn,base

Author

Patrick De Geest, Oct 15 1998

Status

approved