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Minimal nested palindromic base-6 primes with seed 2; see Comments.
3

%I #7 Oct 31 2015 15:02:41

%S 2,525,1252521,512525215,102512525215201,5110251252521520115,

%T 151102512525215201151,5515110251252521520115155,

%U 50551511025125252152011515505,525055151102512525215201151550525,1152505515110251252521520115155052511

%N Minimal nested palindromic base-6 primes with seed 2; 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="/A262649/b262649.txt">Table of n, a(n) for n = 1..300</a>

%e a(3) = 1252521 is the least base-6 prime having a(2) = 525 in its middle. Triangular format:

%e 2

%e 525

%e 1252521

%e 512525215

%e 102512525215201

%e 5110251252521520115

%t s = {2}; 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 (* A262649 *)

%t Map[FromDigits[ToString[#], base] &, s] (* A262650 *)

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

%Y Cf. A261881 (base 10), A262650, A262627.

%K nonn,easy,base

%O 1,1

%A _Clark Kimberling_, Oct 27 2015