cp's OEIS Frontend

A247098 Smallest prime p that generates n different primes if it is inserted into p itself.

%I A247098 #27 Jul 02 2019 05:34:18
%S A247098 2,109,131,10289,12197,1227797,101636629,118561139,10596073217,
%T A247098 89466662147,37898818253
%N A247098 Smallest prime p that generates n different primes if it is inserted into p itself.
%C A247098 a(8) > 10^9.
%C A247098 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 A247098 a(0) = 2 is prime but concat(2,2) = 22 is not.
%e A247098 a(1) = 109 is prime and also concat(1,109,09) = 110909.
%e A247098 a(2) = 131 is prime. Again, concat(13,131,1) = 131311 is prime and also concat(1,131,31) = 113131.
%e A247098 a(5) = 1227797 and the five primes that are generated are: 12277912277977, 12271227797797, 12212277977797, 12122779727797, 11227797227797.
%p A247098 P:=proc(q) local a,b,i,j,k,n,t: print(2); for j from 1 to q do n:=2:
%p A247098 for k from 1 to q do n:=nextprime(n): b:=length(n): t:=0:
%p A247098 for i from 1 to b-1 do if isprime((trunc(n/10^i)*10^b+n)*10^i+(n mod 10^i))
%p A247098 then t:=t+1; fi; od;  if t=j then print(n); break; fi; od; od; end: P(10^9);
%Y A247098 Cf. A250311, A250312.
%K A247098 nonn,base,more
%O A247098 0,1
%A A247098 _Paolo P. Lava_, Nov 18 2014
%E A247098 a(8)-a(10) from _Chai Wah Wu_, Jul 01 2019