A191235 Primes p such that the binary representation of p is the concatenation of the binary representations of prime 2 and an odd prime.

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

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: A199848 A352494 A228444 * A146451 A195043 A029468

Adjacent sequences: A191232 A191233 A191234 * A191236 A191237 A191238

Keyword

nonn,easy,base

Author

Juri-Stepan Gerasimov, May 27 2011

Extensions

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

Status

approved