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Fractal palindromic primes of first order.
5

%I #20 May 19 2024 13:14:50

%S 313,353,373,383,727,757,787,797,11311,11411,1311131,1317131,1513151,

%T 1917191,9196919,9199919,10301110301,10301910301,10501210501,

%U 10501910501,10601110601,12421212421,12421812421,12721612721,13331113331,13331713331,13831913831,13931413931

%N Fractal palindromic primes of first order.

%C A first order fractal palindromic prime is one of the form WmW, where either wing W about a central digit m, is itself a palindromic prime, which, however, may not be further split in this manner to maintain the property.

%C [Log_10(a(n))] must be of the form k2. - _Robert G. Wilson v_, Jul 22 2005

%H Michael S. Branicky, <a href="/A082584/b082584.txt">Table of n, a(n) for n = 1..21046</a> (all terms < 10^26, corresponding to b-file of A082598)

%e 12421812421 is in the sequence because it is a concatenation of the palindromic prime part 12421 with itself, hinging over the central 8;12421 cannot however be split into simpler palindromic primes in this way.

%t f[n_] := Block[{m = n}, pd = IntegerDigits[m]; pd = Take[pd, Floor[Length[pd]/2]]; If[PrimeQ[m] && PrimeQ[FromDigits[pd]] && pd == Reverse[pd] && m == FromDigits[Reverse[IntegerDigits[m]]] && ! f[FromDigits[pd]], True, False]]; Do[ If[ f[n], Print[n]], {n, 10^10}] (* _Robert G. Wilson v_, Jul 22 2005 *)

%Y Cf. A002385.

%K base,nonn

%O 1,1

%A _Lekraj Beedassy_, May 07 2003

%E a(25) and beyond from _Michael S. Branicky_, May 19 2024