A262631 - OEIS

%I #13 Oct 19 2015 05:10:29

%S 1,111,1111111,22111111122,1221111111221,112211111112211,

%T 2111221111111221112,2102111221111111221112012,

%U 1212102111221111111221112012121,20121210211122111111122111201212102,2002201212102111221111111221112012121022002

%N Minimal nested base-3 palindromic primes with seed 1.

%C Using only base-3 digits 0,1,2, 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 base-3 palindromic primes with seed s.

%H Clark Kimberling, <a href="/A262631/b262631.txt">Table of n, a(n) for n = 1..300</a>

%e a(4) = 22111111122 is the least base-3 prime having a(3) = 1111111 in its middle. Triangular format:

%e          1

%e         111

%e       1111111

%e     22111111122

%e    1221111111221

%e   112211111112211

%t s = {1}; base = 3; 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  (* A262631 *)

%t Map[FromDigits[ToString[#], base] &, s]  (* A262632 *)

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

%Y Cf. A261881 (base 10), A262632, A262627. Subset of A117698 (except a(1)).

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Oct 02 2015