

A191235


Primes p such that the binary representation of p is the concatenation of the binary representations of prime 2 and an odd prime.


2



11, 23, 43, 83, 181, 353, 359, 383, 643, 661, 691, 709, 739, 751, 1301, 1307, 1361, 1373, 1433, 1481, 1487, 1511, 1523, 2617, 2647, 2689, 2707, 2731, 2749, 2767, 2791, 2857, 2887, 3001, 3019, 3061, 3067, 5147, 5189, 5297, 5309, 5333, 5387, 5393
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OFFSET

1,1


COMMENTS

The odd primes arising in computing the sequence are 3, 7, 11, 19, 53, 97, 103, 127, 131, 149, 179, 197, 227, 239, ...
Primes whose binary representation equals the binary representation of some prime preceded by 10.  Klaus Brockhaus, May 29 2011


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

11 is in the sequence because 11, 2, 3 in binary are resp. 1011, 10, 11.
83 is in the sequence because 83, 2, 19 in binary are resp. 1010011, 10, 10011.


PROG

(PARI) A053644(n)=my(k=1); while(k<=n, k<<=1); k>>1;
forprime(p=2, 1e3, if(isprime(k=4*A053644(p)+p), print1(k", "))) \\ Charles R Greathouse IV, May 27 2011
(MAGMA) [ p: p in PrimesInInterval(3, 6100)  exists(q){ k: k in PrimesUpTo(p div 3)  Intseq(p, 2) eq Intseq(k, 2) cat [0, 1] } ]; // Klaus Brockhaus, May 29 2011


CROSSREFS

Cf. A004676, A007088, A091932, A080165, A090423, A053644.
Sequence in context: A068842 A199848 A228444 * A146451 A195043 A029468
Adjacent sequences: A191232 A191233 A191234 * A191236 A191237 A191238


KEYWORD

nonn,easy,base


AUTHOR

JuriStepan Gerasimov, May 27 2011


EXTENSIONS

a(4) corrected, a(15)a(56) added by Charles R Greathouse IV, May 27 2011


STATUS

approved



