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

1,1

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

Links

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

Example

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.

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 *)

Crossrefs

Cf. A002385.

Sequence in context: A159574 A139656 A061323 * A088282 A068687 A093808

Adjacent sequences: A082581 A082582 A082583 * A082585 A082586 A082587

Keyword

base,nonn

Author

Lekraj Beedassy, May 07 2003

Extensions

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

Status

approved