%I #10 Oct 02 2015 13:05:44
%S 1300000000031,713000000000317,1471300000000031741,
%T 12147130000000003174121,3121471300000000031741213,
%U 1213121471300000000031741213121,33121312147130000000003174121312133,323312131214713000000000317412131213323
%N Minimal nested palindromic primes with seed 000000000.
%C Let s be a palindrome and put a(1) = s. Let a(2) be the least palindromic prime having s in the middle; for n > 2, let a(n) be the least palindromic prime having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s. (For A260250, the seed is not an integer, so that the offset is 2.)
%H Clark Kimberling, <a href="/A260250/b260250.txt">Table of n, a(n) for n = 2..200</a>
%e As a triangle:
%e 000000000
%e 1300000000031
%e 713000000000317
%e 1471300000000031741
%e 12147130000000003174121,
%e 3121471300000000031741213
%e 1213121471300000000031741213121,
%t s0 = "000000000"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
%t (* _Peter J. C. Moses_, Sep 23 2015 *)
%Y Cf. A261881.
%K nonn,base,easy
%O 2,1
%A _Clark Kimberling_, Sep 24 2015