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 A262633 Minimal nested base-4 palindromic primes with seed 0. 3

%I

%S 0,101,31013,3310133,1023310133201,3331023310133201333,

%T 3223331023310133201333223,1133223331023310133201333223311,

%U 100311332233310233101332013332233113001,10231003113322333102331013320133322331130013201

%N Minimal nested base-4 palindromic primes with seed 0.

%C 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.

%H Clark Kimberling, <a href="/A262633/b262633.txt">Table of n, a(n) for n = 1..300</a>

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

%e 0

%e 101

%e 31013

%e 3310133

%e 1023310133201

%e 3331023310133201333,

%t s = {0}; base = 4; 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 (* A262633 *)

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

%t (* _Peter J. C. Moses_, Sep 01 2015 *)

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

%K nonn,base

%O 1,2

%A _Clark Kimberling_, Oct 02 2015

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Last modified August 17 15:14 EDT 2022. Contains 356189 sequences. (Running on oeis4.)