A244862 Pairs of prime numbers (p,q) starting with a(1)=2 such that p U q (where U denotes concatenation) is a prime number and a(n) is always extended with the smallest available prime not yet present in the sequence.

2, 3, 5, 23, 7, 19, 11, 17, 13, 61, 29, 53, 31, 37, 41, 59, 43, 73, 47, 83, 67, 79, 71, 167, 89, 101, 97, 103, 107, 137, 109, 139, 113, 131, 127, 157, 149, 173, 151, 163, 179, 233, 181, 193, 191, 227, 197, 257, 199, 211, 223, 229, 239, 251, 241, 271, 263, 269, 277

Offset

1,1

Comments

The first pairs are (2,3),(5,23),(7,19),(11,17),(13,61),(29,53)=> 23, 523, 719, 1117, 1361, 2953, ... are prime numbers.

Links

Table of n, a(n) for n=1..59.

Maple

with(numtheory):nn:=60:lst:={2, 3}: printf ( "%d %d \n", 2, 3):
   for a from 2 to nn do:
     p:=ithprime(a):ii:=0:
      for b from 1 to nn while(ii=0)do:
        q:=ithprime(b):s:=p*10^(length(q))+q:
         if type(s, prime)=true and lst intersect {p, q}={}
          then
          lst:=lst union {p, q}:ii:=1:printf(`%d, `, p):printf(`%d, `, q):
          else
        fi:
      od:
    od:

Crossrefs

Cf. A000040, A105184.

Sequence in context: A339228 A013639 A047995 * A338403 A024782 A024775

Adjacent sequences: A244859 A244860 A244861 * A244863 A244864 A244865

Keyword

nonn,base

Author

Michel Lagneau, Jul 25 2014

Status

approved