login
Minimal nested palindromic base-6 primes with seed 3; see Comments.
4

%I #6 Oct 31 2015 15:03:02

%S 3,11311,121131121,5312113112135,14531211311213541,

%T 1145312113112135411,51114531211311213541115,

%U 5511145312113112135411155,50551114531211311213541115505,115055111453121131121354111550511,51150551114531211311213541115505115

%N Minimal nested palindromic base-6 primes with seed 3; see Comments.

%C Using only base-6 digits 0,1,2,3,4,5, 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-6 primes with seed s.

%H Clark Kimberling, <a href="/A262651/b262651.txt">Table of n, a(n) for n = 1..300</a>

%e a(3) = 121131121 is the least base-6 prime having a(2) = 11311 in its middle. Triangular format:

%e 3

%e 11311

%e 121131121

%e 5312113112135

%e 14531211311213541

%t s = {3}; base = 6; 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 (* A262651 *)

%t Map[FromDigits[ToString[#], base] &, s] (* A262652 *)

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

%Y Cf. A261881 (base 10), A262652, A262627.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 27 2015