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Minimal nested palindromic primes with seed 00000.
2

%I #14 Nov 03 2015 07:29:29

%S 140000041,31400000413,9314000004139,74931400000413947,

%T 3749314000004139473,937493140000041394739,3693749314000004139473963,

%U 10369374931400000413947396301,351036937493140000041394739630153,7035103693749314000004139473963015307

%N Minimal nested palindromic primes with seed 00000.

%C 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. (For A252532, the seed is not an integer, so that the offset is 2.)

%H Clark Kimberling, <a href="/A262532/b262532.txt">Table of n, a(n) for n = 2..200</a>

%e As a triangle:

%e 00000

%e 140000041

%e 31400000413

%e 9314000004139

%e 74931400000413947

%e 3749314000004139473

%e 937493140000041394739

%t s0 = "00000"; 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}]

%t (* _Peter J. C. Moses_, Sep 23 2015 *)

%Y Cf. A261881.

%K nonn,base,easy

%O 2,1

%A _Clark Kimberling_, Sep 24 2015