A034808 Concatenation of 'prevprime(k) and k' 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: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• base

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

Examples

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

Links

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

Crossrefs

Cf. A034809-A034821.

Cf. A151799, A007917.

Programs

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 *)

PARI

isok(n)=n>2 && isprime(fromdigits(concat(digits(precprime(n-1)), digits(n)))) \\ Andrew Howroyd, Aug 13 2024

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

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024