cp's OEIS Frontend

A068684 Primes obtained as a concatenation p,q,p where p and q are successive primes and p

%I A068684 #18 Jul 02 2025 11:30:33
%S A068684 353,131713,171917,192319,293129,374137,434743,596159,677167,
%T A068684 139149139,163167163,179181179,223227223,229233229,269271269,
%U A068684 281283281,347349347,379383379,547557547,683691683,761769761,857859857,863877863,102110311021,103910491039,108710911087,109110931091,109310971093
%N A068684 Primes obtained as a concatenation p,q,p where p and q are successive primes and p<q.
%H A068684 Robert Israel, <a href="/A068684/b068684.txt">Table of n, a(n) for n = 1..10000</a>
%e A068684 171917 is a prime which is the concatenation of 17, 19 and 17.
%p A068684 cat3:= proc(a,b,c) local alpha,beta;
%p A068684     beta:= ilog10(c)+1;
%p A068684     alpha:= beta + ilog10(b)+1;
%p A068684     10^alpha*a + 10^beta*b + c
%p A068684 end proc:
%p A068684 R:= NULL: count:= 0: q:= 2:
%p A068684 while count < 100 do
%p A068684   p:= q; q:= nextprime(q);
%p A068684   v:= cat3(p,q,p);
%p A068684   if isprime(v) then R:= R,v; count:= count+1;
%p A068684   fi
%p A068684 od:
%p A068684 R; # _Robert Israel_, Jul 01 2025
%o A068684 (PARI) f(n)=prime(n)*(10^(ceil(log(prime(n+1))/log(10))+ceil(log(prime(n))/log(10))))+ prime(n+1)*10^ceil(log(prime(n))/log(10))+prime(n);
%o A068684 for(n=1,300, if(isprime(f(n))==1, print1(f(n),", ")))
%Y A068684 Cf. A068683, A078350.
%K A068684 base,nonn
%O A068684 1,1
%A A068684 _Amarnath Murthy_, Mar 02 2002
%E A068684 More terms from _Benoit Cloitre_, Mar 21 2002
%E A068684 More terms from _Robert Israel_, Jul 02 2025