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A262627 Minimal nested base-2 palindromic primes with seed 0.

%I A262627 #11 Oct 17 2015 16:46:06
%S A262627 0,101,11001010011,101100101001101,10101011001010011010101,
%T A262627 111010101100101001101010111,1111101010110010100110101011111,
%U A262627 101111111010101100101001101010111111101,110101111111010101100101001101010111111101011
%N A262627 Minimal nested base-2 palindromic primes with seed 0.
%C A262627 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 A262627 Guide to related sequences
%C A262627 base  seed   base-b repr.    base-10 repr.
%C A262627 2         0      A262627        A262628
%C A262627 2         1      A262629        A262630
%C A262627 3         1      A262631        A262632
%C A262627 4         0      A262633        A262634
%C A262627 4         1      A262635        A262636
%C A262627 4         2      A262637        A262638
%C A262627 4         3      A262639        A262640
%C A262627 5         1      A262641        A262642
%C A262627 5         3      A262643        A262644
%C A262627 6         0      A262645        A262646
%C A262627 6         1      A262647        A262648
%C A262627 6         2      A262649        A262650
%C A262627 6         3      A262651        A262652
%C A262627 6         4      A262653        A262654
%C A262627 6         5      A262655        A262656
%C A262627 7         1      A262657        A262658
%C A262627 8         0      A262659        A262660
%C A262627 8         1      A262661        A262662
%C A262627 10        0      A261881        A261881
%C A262627 10        1      A261818        A261818
%H A262627 Clark Kimberling, <a href="/A262627/b262627.txt">Table of n, a(n) for n = 1..300</a>
%e A262627 a(3) = 11001010011 =A117697(15) is the least prime having a(2) = 101 in its middle. Triangular format:
%e A262627                0
%e A262627               101
%e A262627           11001010011
%e A262627         101100101001101
%e A262627     10101011001010011010101
%e A262627   111010101100101001101010111
%e A262627 1111101010110010100110101011111
%t A262627 s = {0}; base = 2; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
%t A262627 AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s  (* A262627 *)
%t A262627 Map[FromDigits[ToString[#], base] &, s]  (* A262628 *)
%t A262627 (* _Peter J. C. Moses_, Sep 01 2015 *)
%Y A262627 Cf. A117697, A261881 (base 10), A262628-A262662.
%K A262627 nonn,base
%O A262627 1,2
%A A262627 _Clark Kimberling_, Oct 02 2015