%I #11 Oct 17 2015 16:46:06

%S 0,101,11001010011,101100101001101,10101011001010011010101,

%T 111010101100101001101010111,1111101010110010100110101011111,

%U 101111111010101100101001101010111111101,110101111111010101100101001101010111111101011

%N Minimal nested base-2 palindromic primes with seed 0.

%C Using only base-2 digits 0 and 1, 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-2 palindromic primes with seed s -- a(1) being not prime, of course.

%C Guide to related sequences

%C base seed base-b repr. base-10 repr.

%C 2 0 A262627 A262628

%C 2 1 A262629 A262630

%C 3 1 A262631 A262632

%C 4 0 A262633 A262634

%C 4 1 A262635 A262636

%C 4 2 A262637 A262638

%C 4 3 A262639 A262640

%C 5 1 A262641 A262642

%C 5 3 A262643 A262644

%C 6 0 A262645 A262646

%C 6 1 A262647 A262648

%C 6 2 A262649 A262650

%C 6 3 A262651 A262652

%C 6 4 A262653 A262654

%C 6 5 A262655 A262656

%C 7 1 A262657 A262658

%C 8 0 A262659 A262660

%C 8 1 A262661 A262662

%C 10 0 A261881 A261881

%C 10 1 A261818 A261818

%H Clark Kimberling, <a href="/A262627/b262627.txt">Table of n, a(n) for n = 1..300</a>

%e a(3) = 11001010011 =A117697(15) is the least prime having a(2) = 101 in its middle. Triangular format:

%e 0

%e 101

%e 11001010011

%e 101100101001101

%e 10101011001010011010101

%e 111010101100101001101010111

%e 1111101010110010100110101011111

%t s = {0}; base = 2; 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 (* A262627 *)

%t Map[FromDigits[ToString[#], base] &, s] (* A262628 *)

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

%Y Cf. A117697, A261881 (base 10), A262628-A262662.

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Oct 02 2015