A163498 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.

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

Offset

1,1

Comments

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

Links

Chai Wah Wu, Table of n, a(n) for n = 1..2000

Example

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.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A163499.

Sequence in context: A107715 A090707 A062350 * A038874 A164624 A215819

Adjacent sequences: A163495 A163496 A163497 * A163499 A163500 A163501

Keyword

base,nonn

Author

Leroy Quet, Jul 29 2009

Extensions

More terms from Stefan Steinerberger, Aug 05 2009

More terms from Chai Wah Wu, Jul 28 2014

Status

approved