A247098 - OEIS

%I #27 Jul 02 2019 05:34:18

%S 2,109,131,10289,12197,1227797,101636629,118561139,10596073217,

%T 89466662147,37898818253

%N Smallest prime p that generates n different primes if it is inserted into p itself.

%C a(8) > 10^9.

%C The concatenation of p with p will not result in a prime as the result is divisible by 10^k+1, where k is the number of digits in p. - _Chai Wah Wu_, Jun 25 2019

%e a(0) = 2 is prime but concat(2,2) = 22 is not.

%e a(1) = 109 is prime and also concat(1,109,09) = 110909.

%e a(2) = 131 is prime. Again, concat(13,131,1) = 131311 is prime and also concat(1,131,31) = 113131.

%e a(5) = 1227797 and the five primes that are generated are: 12277912277977, 12271227797797, 12212277977797, 12122779727797, 11227797227797.

%p P:=proc(q) local a,b,i,j,k,n,t: print(2); for j from 1 to q do n:=2:

%p for k from 1 to q do n:=nextprime(n): b:=length(n): t:=0:

%p for i from 1 to b-1 do if isprime((trunc(n/10^i)*10^b+n)*10^i+(n mod 10^i))

%p then t:=t+1; fi; od;  if t=j then print(n); break; fi; od; od; end: P(10^9);

%Y Cf. A250311, A250312.

%K nonn,base,more

%O 0,1

%A _Paolo P. Lava_, Nov 18 2014

%E a(8)-a(10) from _Chai Wah Wu_, Jul 01 2019