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A068683 Primes formed by the concatenation p,q,p where p and q are successive primes and p>q.

%I A068683 #17 Jul 02 2025 11:30:23
%S A068683 757,131113,171317,231923,312931,474347,978997,10197101,107103107,
%T A068683 127113127,139137139,151149151,167163167,367359367,421419421,
%U A068683 433431433,461457461,617613617,643641643,701691701,863859863,911907911,991983991,102110191021,103110211031,103310311033,104910391049
%N A068683 Primes formed by the concatenation p,q,p where p and q are successive primes and p>q.
%H A068683 Robert Israel, <a href="/A068683/b068683.txt">Table of n, a(n) for n = 1..10000</a>
%e A068683 171317 is a prime which is the concatenation of 17, 13 and 17.
%p A068683 cat3:= proc(a,b,c) local alpha,beta;
%p A068683     beta:= ilog10(c)+1;
%p A068683     alpha:= beta + ilog10(b)+1;
%p A068683     10^alpha*a + 10^beta*b + c
%p A068683 end proc:
%p A068683 R:= NULL: count:= 0: p:= 2:
%p A068683 while count < 100 do
%p A068683   q:= p; p:= nextprime(p);
%p A068683   v:= cat3(p,q,p);
%p A068683   if isprime(v) then R:= R,v; count:= count+1;
%p A068683   fi
%p A068683 od:
%p A068683 R; # _Robert Israel_, Jul 01 2025
%t A068683 Select[FromDigits[Flatten[IntegerDigits/@#]]&/@({Last[#],First[#], Last[#]} &/@Partition[Prime[Range[200]],2,1]),PrimeQ] (* _Harvey P. Dale_, Oct 25 2011 *)
%K A068683 base,nonn
%O A068683 1,1
%A A068683 _Amarnath Murthy_, Mar 02 2002
%E A068683 More terms from _Sascha Kurz_, Mar 26 2002
%E A068683 More terms from _Robert Israel_, Jul 02 2025