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%I #32 Mar 14 2023 10:02:32
%S 5,1097,2237,2689,3541,12979,13477,22367,22783,27701,28499,33521,
%T 33613,43093,51839,55487,57383,65423,69931,70201,71429,74209,80599,
%U 82267,82889,83591,95009,99079,99881,105929,122201,123923,125261
%N Primes p such that the decimal expansion of p remains prime under two iterations of base-10 to base-2 conversions.
%C More precisely, "... remains prime under two iterations of base-10 to base-2 conversions, but not three iterations."
%C .
%H Sebastian Petzelberger, <a href="/A123266/b123266.txt">Table of n, a(n) for n = 1..10000</a>.
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_280.htm">Puzzle 280. 3893257</a>, The Prime Puzzles & Problems Connection.
%e 5 is a term because 5_10 = 101_2 and 101_10 = 1100101_2 and both 101 and 1100101 are prime in base 10.
%t okQ[n_] := And @@ PrimeQ[Rest[NestList[FromDigits[IntegerDigits[#, 2]] &, n, 2]]]; Select[Prime[Range[20000]], okQ] (* _Harvey P. Dale_, Jan 14 2011 *)
%o (PARI) A007088(n)=fromdigits(binary(n),10)
%o is(n)=isprime(n) && isprime(n=A007088(n)) && isprime(A007088(n)) \\ _Charles R Greathouse IV_, Apr 08 2015
%Y Cf. A065720, A007088, A256621, A256622.
%K base,nonn
%O 1,1
%A _Martin Raab_, Oct 09 2006
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