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A262629
Minimal nested base-2 palindromic primes with seed 1.
3
1, 111, 11111, 1111111, 1001111111001, 1001001111111001001, 111110010011111110010011111, 111111110010011111110010011111111, 100111111110010011111110010011111111001, 1011010011111111001001111111001001111111100101101
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.
LINKS
EXAMPLE
a(5) = 1001111111001 = A117697(20) is the least base-2 prime having a(4) = 1111111 = A117697(8) in its middle. Triangular format:
1
111
11111
1111111
1001111111001
1001001111111001001
111110010011111110010011111
MATHEMATICA
s = {1}; 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 (* A262629 *)
Map[FromDigits[ToString[#], base] &, s] (* A262630 *)
(* Peter J. C. Moses, Sep 01 2015 *)
CROSSREFS
Cf. A261881 (base 10), A262627. Subsequence of A117697 (expect a(1)).
Sequence in context: A138146 A100706 A259102 * A111864 A098034 A109242
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Oct 02 2015
STATUS
approved