|
%I #53 Sep 21 2019 05:45:33
%S 3,131,10301,1003001,100030001,10070307001,1000703070001,
%T 100075030570001,10006750305760001,1000167503057610001,
%U 100015675030576510001,10001056750305765010001,1000105367503057635010001,100001053675030576350100001,10000105360750305706350100001
%N a(1) = 3, a(n) = smallest palindromic prime obtained by inserting two paired digits anywhere in a(n-1).
%C With the exception of 11, all decimal palindromic numbers with an even number of digits are composite (they are divisible by 11). This leaves only odd-digit-length palindromes, therefore (at least) a pair of digits needs to be inserted at every iteration.
%C The sequence terminates at a(19) = 1000010025136075033305706315200100001, which cannot be extended to another palindromic prime by inserting two paired digits. - _Giovanni Resta_, Sep 20 2019
%H Giovanni Resta, <a href="/A082622/b082622.txt">Table of n, a(n) for n = 1..19</a>
%o (PARI) \\ Warning: program gives incorrect results; _Michel Marcus_, Sep 21 2019
%o {w=[];print(1" "3);
%o for(i=2,58,w=concat(0,w);for(pos=1,i,if(pos>1,w[pos-1]=w[pos]);
%o for(d=0,9,w[pos]=d;
%o if(isprime(n=fromdigits(concat(Vecrev(w),concat(3,w)))),
%o print(i" "n);break(2)))))} \\ _Serge Batalov_, Dec 18 2015
%Y Cf. A082620, A082621.
%K nonn,base,fini,full
%O 1,1
%A _Amarnath Murthy_, Apr 29 2003
%E a(6)-a(56) from _Serge Batalov_, Dec 18 2015
%E Terms following a(6) corrected by _Giovanni Resta_, Sep 20 2019
|
