A082584 Fractal palindromic primes of first order.

313, 353, 373, 383, 727, 757, 787, 797, 11311, 11411, 1311131, 1317131, 1513151, 1917191, 9196919, 9199919, 10301110301, 10301910301, 10501210501, 10501910501, 10601110601, 12421212421, 12421812421, 12721612721, 13331113331, 13331713331, 13831913831, 13931413931

Offset: 1

Author

Lekraj Beedassy, May 07 2003

Keywords

• base
• nonn

Comments

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.

[Log_10(a(n))] must be of the form k2. - Robert G. Wilson v, Jul 22 2005

Examples

			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.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..21046 (all terms < 10^26, corresponding to b-file of A082598)

Crossrefs

Cf. A002385.

Programs

Mathematica

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 *)

Extensions

a(25) and beyond from Michael S. Branicky, May 19 2024