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

353, 131713, 171917, 192319, 293129, 374137, 434743, 596159, 677167, 139149139, 163167163, 179181179, 223227223, 229233229, 269271269, 281283281, 347349347, 379383379, 547557547, 683691683, 761769761, 857859857, 863877863, 102110311021, 103910491039, 108710911087, 109110931091, 109310971093

Offset: 1

Author

Amarnath Murthy, Mar 02 2002

Keywords

• base
• nonn

Examples

			171917 is a prime which is the concatenation of 17, 19 and 17.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068683, A078350.

Programs

Maple

cat3:= proc(a,b,c) local alpha,beta;
    beta:= ilog10(c)+1;
    alpha:= beta + ilog10(b)+1;
    10^alpha*a + 10^beta*b + c
end proc:
R:= NULL: count:= 0: q:= 2:
while count < 100 do
  p:= q; q:= nextprime(q);
  v:= cat3(p,q,p);
  if isprime(v) then R:= R,v; count:= count+1;
  fi
od:
R; # Robert Israel, Jul 01 2025

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);
for(n=1,300, if(isprime(f(n))==1, print1(f(n),", ")))

Extensions

More terms from Benoit Cloitre, Mar 21 2002

More terms from Robert Israel, Jul 02 2025