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A262657 Minimal nested palindromic base-7 primes with seed 1; see Comments.

%I A262657 #6 Oct 31 2015 15:11:19
%S A262657 1,212,42124,204212402,2220421240222,222204212402222,
%T A262657 2222220421240222222,12222222042124022222221,
%U A262657 3122222220421240222222213,331222222204212402222222133,53312222222042124022222221335,165331222222204212402222222133561
%N A262657 Minimal nested palindromic base-7 primes with seed 1; see Comments.
%C A262657 Using only base-7 digits 0,1,2,3,4,5,6 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 have a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic base-7 primes with seed s.
%H A262657 Clark Kimberling, <a href="/A262657/b262657.txt">Table of n, a(n) for n = 1..300</a>
%e A262657 a(3) = 42124 is the least base-7 prime having a(2) = 212 in its middle. Triangular format:
%e A262657          1
%e A262657         212
%e A262657        42124
%e A262657      204212402
%e A262657    2220421240222
%e A262657   222204212402222
%e A262657 2222220421240222222
%t A262657 s = {1}; base = 7; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262657 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262657 *)
%t A262657 Map[FromDigits[ToString[#], base] &, s]  (* A262658 *)
%t A262657 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262657 Cf. A261881 (base 10), A262658, A262627.
%K A262657 nonn,easy,base
%O A262657 1,2
%A A262657 _Clark Kimberling_, Oct 27 2015