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A123266
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Primes p such that the decimal expansion of p remains prime under two iterations of base-10 to base-2 conversions.
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5
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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
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OFFSET
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1,1
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COMMENTS
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More precisely, "... remains prime under two iterations of base-10 to base-2 conversions, but not three iterations."
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LINKS
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EXAMPLE
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5 is a term because 5_10 = 101_2 and 101_10 = 1100101_2 and both 101 and 1100101 are prime in base 10.
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MATHEMATICA
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okQ[n_] := And @@ PrimeQ[Rest[NestList[FromDigits[IntegerDigits[#, 2]] &, n, 2]]]; Select[Prime[Range[20000]], okQ] (* Harvey P. Dale, Jan 14 2011 *)
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PROG
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(PARI) A007088(n)=fromdigits(binary(n), 10)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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