A262499 Minimal nested palindromic primes with seed 111111111.

111111111, 1311111111131, 31131111111113113, 3311311111111131133, 333113111111111311333, 3033311311111111131133303, 1323033311311111111131133303231, 313230333113111111111311333032313, 9531323033311311111111131133303231359

Offset: 1

Author

Clark Kimberling, Sep 24 2015

Keywords

• nonn
• base
• easy

Comments

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 having a(n-1) in the middle. Then (a(n)) is the sequence of minimal nested palindromic primes with seed s.

Examples

			As a triangle:
              111111111
            1311111111131
          31131111111113113
         3311311111111131133
        333113111111111311333
      3033311311111111131133303
   1323033311311111111131133303231
  313230333113111111111311333032313
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A261881.

Programs

Mathematica

s0 = "111111111"; s = {ToExpression[s0]};Do[NestWhile[# + 1 &, 1, ! PrimeQ[tmp = FromDigits[Join[#, IntegerDigits[Last[s], 10, Max[StringLength[s0],Length[IntegerDigits[Last[s]]]]], Reverse[#]]&[IntegerDigits[#]]]] &]; AppendTo[s, tmp], {10}]; s0 <> ", " <> StringTake[ToString[Rest[s]], {2, -2}]
(* Peter J. C. Moses, Sep 23 2015 *)