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

Author

Juri-Stepan Gerasimov, May 27 2011

Keywords

• nonn
• easy
• base

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A004676, A007088, A091932, A080165, A090423, A053644.

Programs

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

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

Extensions

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