A123266 Primes p such that the decimal expansion of p remains prime under two iterations of base-10 to base-2 conversions.

5, 1097, 2237, 2689, 3541, 12979, 13477, 22367, 22783, 27701, 28499, 33521, 33613, 43093, 51839, 55487, 57383, 65423, 69931, 70201, 71429, 74209, 80599, 82267, 82889, 83591, 95009, 99079, 99881, 105929, 122201, 123923, 125261

Offset: 1

Author

Martin Raab, Oct 09 2006

Keywords

• base
• nonn

Comments

More precisely, "... remains prime under two iterations of base-10 to base-2 conversions, but not three iterations."

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Examples

			5 is a term because 5_10 = 101_2 and 101_10 = 1100101_2 and both 101 and 1100101 are prime in base 10.
		

Links

• Sebastian Petzelberger, Table of n, a(n) for n = 1..10000.
• Carlos Rivera, Puzzle 280. 3893257, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A065720, A007088, A256621, A256622.

Programs

Mathematica

okQ[n_] := And @@ PrimeQ[Rest[NestList[FromDigits[IntegerDigits[#, 2]] &, n, 2]]]; Select[Prime[Range[20000]], okQ] (* Harvey P. Dale, Jan 14 2011 *)

PARI

A007088(n)=fromdigits(binary(n),10)
is(n)=isprime(n) && isprime(n=A007088(n)) && isprime(A007088(n)) \\ Charles R Greathouse IV, Apr 08 2015