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A262633 Minimal nested base-4 palindromic primes with seed 0. 3
0, 101, 31013, 3310133, 1023310133201, 3331023310133201333, 3223331023310133201333223, 1133223331023310133201333223311, 100311332233310233101332013332233113001, 10231003113322333102331013320133322331130013201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Using only base-4 digits 0,1,2,3, 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-4 palindromic primes with seed s.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..300

EXAMPLE

a(3) = 31013 is the least base-4 prime having a(2) = 101 in its middle. Triangular format:

         0

        101

       31013

      3310133

   1023310133201

3331023310133201333,

MATHEMATICA

s = {0}; base = 4; 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  (* A262633 *)

Map[FromDigits[ToString[#], base] &, s]  (* A262634 *)

(* Peter J. C. Moses, Sep 01 2015 *)

CROSSREFS

Cf. A261881 (base 10), A262634, A262627. Subsequence of A117699.

Sequence in context: A327741 A183056 A261881 * A261966 A076127 A180053

Adjacent sequences:  A262630 A262631 A262632 * A262634 A262635 A262636

KEYWORD

nonn,base

AUTHOR

Clark Kimberling, Oct 02 2015

STATUS

approved

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)