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A163498
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Those primes p that after each is written in binary, and a 0 is inserted before every 1, then the value of this new number is also prime.
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2
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2, 3, 11, 13, 23, 37, 43, 59, 79, 89, 103, 109, 113, 139, 149, 181, 193, 197, 227, 239, 263, 269, 281, 283, 307, 401, 433, 443, 449, 457, 463, 503, 523, 547, 587, 617, 653, 673, 691, 811, 821, 823, 829, 839, 877, 887, 911, 937, 967, 1021, 1049, 1061, 1063
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OFFSET
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1,1
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COMMENTS
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Equal to primes p such that when written in binary, and a 0 is inserted after every binary digit 1, results in 2 times a prime number. For example, 13 is in the list as 13 is 1101 in binary. Inserting 0 after every 1 results in 1010010 = 82 decimal, which is 2*41 and 41 is prime. - Chai Wah Wu, Jul 29 2014
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LINKS
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EXAMPLE
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13 in binary is 1101. Insert a 0 before every 1, and we have 0101001, which is 41 in decimal (ignoring the leading 0 in the binary representation). Since 41 is also prime, then 13 is included in this sequence.
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MATHEMATICA
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a = {}; For[n = 1, n < 1000, n++, b = IntegerDigits[Prime[n], 2]; c = {}; For[k = 1, k < Length[b] + 1, k++, AppendTo[c, 0]; If[b[[k]] == 1, AppendTo[c, 1]]]; If[PrimeQ[FromDigits[c, 2]], AppendTo[a, Prime[n]]]]; a (* Stefan Steinerberger, Aug 05 2009 *)
Select[Prime[Range[200]], PrimeQ[FromDigits[Flatten[IntegerDigits[#, 2]/.(1-> {0, 1})], 2]]&] (* Harvey P. Dale, Aug 22 2018 *)
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PROG
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(Python) from sympy import prime, isprime
[prime(n) for n in range(1, 1000) if isprime(int(bin(prime(n)).replace('1', '01'), 2))] # Chai Wah Wu, Jul 28 2014
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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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EXTENSIONS
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STATUS
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approved
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