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A082622 a(1) = 3, a(n) = smallest palindromic prime obtained by inserting two paired digits anywhere in a(n-1). 6
3, 131, 10301, 1003001, 100030001, 10070307001, 1000703070001, 100075030570001, 10006750305760001, 1000167503057610001, 100015675030576510001, 10001056750305765010001, 1000105367503057635010001, 100001053675030576350100001, 10000105360750305706350100001 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 22:22 EST 2022. Contains 350654 sequences. (Running on oeis4.)