A244862 List of pairs of prime numbers (p,q) starting with (2, 3) such that p || q (where || denotes concatenation) is a prime number and the sequence is always extended with the smallest 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, 331, 281, 317, 283, 397, 293, 311, 307, 337, 313, 373, 347, 359, 349, 379, 353

Offset: 1

Author

Michel Lagneau, Jul 25 2014

Keywords

• nonn
• base
• tabf

Examples

			The first few pairs are (2,3),(5,23),(7,19),(11,17),(13,61),(29,53), ..., giving the primes 23, 523, 719, 1117, 1361, 2953, ...
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A105184.

A373794 is a very similar sequence (they first differ at term 69).

Programs

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:
[I have been informed that this program may be incorrect. - N. J. A. Sloane, Jul 03 2024]
# alternative version
P:=proc(q) local a,b,k,i,j,n,ok; a:=[2,3];
for n from 1 to q do k:=3; ok:=1; for i do if ok=1 then k:=nextprime(k);
if numboccur(k,a)=0 then b:=k;
for j from k do k:=nextprime(k); if numboccur(k,a)=0 then
if isprime(b*10^length(k)+k) then a:=[op(a),b,k]; ok:=0; break; fi; fi; od; fi;
else break;fi; od; od; print(op(a)); end: P(500);	# Paolo P. Lava, Jul 03 2024

Extensions

Edited by N. J. A. Sloane, Jul 03 2024. More than the usual number of terms are shown in order to distinguish this from A373794.