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Minimal nested palindromic base-7 primes with seed 1; see Comments.
3

%I #6 Oct 31 2015 15:11:19

%S 1,212,42124,204212402,2220421240222,222204212402222,

%T 2222220421240222222,12222222042124022222221,

%U 3122222220421240222222213,331222222204212402222222133,53312222222042124022222221335,165331222222204212402222222133561

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

%C 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 Clark Kimberling, <a href="/A262657/b262657.txt">Table of n, a(n) for n = 1..300</a>

%e a(3) = 42124 is the least base-7 prime having a(2) = 212 in its middle. Triangular format:

%e 1

%e 212

%e 42124

%e 204212402

%e 2220421240222

%e 222204212402222

%e 2222220421240222222

%t s = {1}; base = 7; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];

%t AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s (* A262657 *)

%t Map[FromDigits[ToString[#], base] &, s] (* A262658 *)

%t (* _Peter J. C. Moses_, Sep 01 2015 *)

%Y Cf. A261881 (base 10), A262658, A262627.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Oct 27 2015