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A082584
Fractal palindromic primes of first order.
5
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
KEYWORD
base,nonn
AUTHOR
Lekraj Beedassy, May 07 2003
EXTENSIONS
a(25) and beyond from Michael S. Branicky, May 19 2024
STATUS
approved