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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

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OFFSET

1,1

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 = 1..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)))]