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%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
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