A082622 a(1) = 3, a(n) = smallest palindromic prime obtained by inserting two paired digits anywhere in a(n-1).

3, 131, 10301, 1003001, 100030001, 10070307001, 1000703070001, 100075030570001, 10006750305760001, 1000167503057610001, 100015675030576510001, 10001056750305765010001, 1000105367503057635010001, 100001053675030576350100001, 10000105360750305706350100001

Offset

1,1

Comments

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.

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..19

Prog

(PARI) \\ Warning: program gives incorrect results; Michel Marcus, Sep 21 2019
{w=[]; print(1" "3);
for(i=2, 58, w=concat(0, w); for(pos=1, i, if(pos>1, w[pos-1]=w[pos]);
for(d=0, 9, w[pos]=d;
if(isprime(n=fromdigits(concat(Vecrev(w), concat(3, w)))),
print(i" "n); break(2)))))} \\ Serge Batalov, Dec 18 2015

Crossrefs

Cf. A082620, A082621.

Sequence in context: A005175 A347985 A082439 * A332113 A075597 A262639

Adjacent sequences: A082619 A082620 A082621 * A082623 A082624 A082625

Keyword

nonn,base,fini,full

Author

Amarnath Murthy, Apr 29 2003

Extensions

a(6)-a(56) from Serge Batalov, Dec 18 2015

Terms following a(6) corrected by Giovanni Resta, Sep 20 2019

Status

approved