cp's OEIS Frontend

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.

%I A244862 #70 Jul 03 2024 20:06:40
%S A244862 2,3,5,23,7,19,11,17,13,61,29,53,31,37,41,59,43,73,47,83,67,79,71,167,
%T A244862 89,101,97,103,107,137,109,139,113,131,127,157,149,173,151,163,179,
%U A244862 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
%N 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.
%H A244862 Paolo P. Lava, <a href="/A244862/b244862.txt">Table of n, a(n) for n = 1..1000</a>
%e A244862 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, ...
%p A244862 with(numtheory):nn:=60:lst:={2,3}: printf ( "%d %d \n",2,3):
%p A244862    for a from 2 to nn do:
%p A244862      p:=ithprime(a):ii:=0:
%p A244862       for b from 1 to nn while(ii=0)do:
%p A244862         q:=ithprime(b):s:=p*10^(length(q))+q:
%p A244862          if type(s,prime)=true and lst intersect {p,q}={}
%p A244862           then
%p A244862           lst:=lst union {p,q}:ii:=1:printf(`%d, `,p):printf(`%d, `,q):
%p A244862           else
%p A244862         fi:
%p A244862       od:
%p A244862     od:
%p A244862 [I have been informed that this program may be incorrect. - _N. J. A. Sloane_, Jul 03 2024]
%p A244862 # alternative version
%p A244862 P:=proc(q) local a,b,k,i,j,n,ok; a:=[2,3];
%p A244862 for n from 1 to q do k:=3; ok:=1; for i do if ok=1 then k:=nextprime(k);
%p A244862 if numboccur(k,a)=0 then b:=k;
%p A244862 for j from k do k:=nextprime(k); if numboccur(k,a)=0 then
%p A244862 if isprime(b*10^length(k)+k) then a:=[op(a),b,k]; ok:=0; break; fi; fi; od; fi;
%p A244862 else break;fi; od; od; print(op(a)); end: P(500);	# _Paolo P. Lava_, Jul 03 2024
%Y A244862 Cf. A000040, A105184.
%Y A244862 A373794 is a very similar sequence (they first differ at term 69).
%K A244862 nonn,base,tabf
%O A244862 1,1
%A A244862 _Michel Lagneau_, Jul 25 2014
%E A244862 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.