OFFSET
1,2
COMMENTS
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.
Guide to related sequences
base seed base-b repr. base-10 repr.
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..300
EXAMPLE
a(3) = 11001010011 =A117697(15) is the least prime having a(2) = 101 in its middle. Triangular format:
0
101
11001010011
101100101001101
10101011001010011010101
111010101100101001101010111
1111101010110010100110101011111
MATHEMATICA
s = {0}; base = 2; z = 20; Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s]], Reverse[#]] &[IntegerDigits[#, base]], base]] &];
AppendTo[s, FromDigits[IntegerDigits[tmp, base]]], {z}]; s (* A262627 *)
Map[FromDigits[ToString[#], base] &, s] (* A262628 *)
(* Peter J. C. Moses, Sep 01 2015 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Oct 02 2015
STATUS
approved