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A262635
Minimal nested base-4 palindromic primes with seed 1.
3
1, 12121, 111212111, 31112121113, 133111212111331, 123133111212111331321, 303123133111212111331321303, 3030312313311121211133132130303, 30303031231331112121113313213030303, 3303030312313311121211133132130303033, 11330303031231331112121113313213030303311
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
EXAMPLE
a(3) = 111212111 is the least base-4 prime having a(2) = 12121 in its middle. Triangular format:
1
12121
111212111
31112121113
133111212111331
123133111212111331321
MATHEMATICA
s = {1}; 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 (* A262635 *)
Map[FromDigits[ToString[#], base] &, s] (* A262636 *)
(* Peter J. C. Moses, Sep 01 2015 *)
CROSSREFS
Cf. A261881 (base 10), A262636, A262627. Subsequence of A117699.
Sequence in context: A031661 A371952 A247403 * A186564 A247690 A126847
KEYWORD
nonn,base
AUTHOR
Clark Kimberling, Oct 02 2015
STATUS
approved