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A262631
Minimal nested base-3 palindromic primes with seed 1.
3
1, 111, 1111111, 22111111122, 1221111111221, 112211111112211, 2111221111111221112, 2102111221111111221112012, 1212102111221111111221112012121, 20121210211122111111122111201212102, 2002201212102111221111111221112012121022002
OFFSET
1,2
COMMENTS
Using only base-3 digits 0,1,2, 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-3 palindromic primes with seed s.
LINKS
EXAMPLE
a(4) = 22111111122 is the least base-3 prime having a(3) = 1111111 in its middle. Triangular format:
1
111
1111111
22111111122
1221111111221
112211111112211
MATHEMATICA
s = {1}; base = 3; 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 (* A262631 *)
Map[FromDigits[ToString[#], base] &, s] (* A262632 *)
(* Peter J. C. Moses, Sep 01 2015 *)
CROSSREFS
Cf. A261881 (base 10), A262632, A262627. Subset of A117698 (except a(1)).
Sequence in context: A242646 A242645 A262647 * A259747 A176194 A261820
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Oct 02 2015
STATUS
approved