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%I #15 Sep 08 2022 08:45:57
%S 11,23,43,83,181,353,359,383,643,661,691,709,739,751,1301,1307,1361,
%T 1373,1433,1481,1487,1511,1523,2617,2647,2689,2707,2731,2749,2767,
%U 2791,2857,2887,3001,3019,3061,3067,5147,5189,5297,5309,5333,5387,5393
%N Primes p such that the binary representation of p is the concatenation of the binary representations of prime 2 and an odd prime.
%C The odd primes arising in computing the sequence are 3, 7, 11, 19, 53, 97, 103, 127, 131, 149, 179, 197, 227, 239, ...
%C Primes whose binary representation equals the binary representation of some prime preceded by 10. - _Klaus Brockhaus_, May 29 2011
%H Charles R Greathouse IV, <a href="/A191235/b191235.txt">Table of n, a(n) for n = 1..10000</a>
%e 11 is in the sequence because 11, 2, 3 in binary are resp. 1011, 10, 11.
%e 83 is in the sequence because 83, 2, 19 in binary are resp. 1010011, 10, 10011.
%o (PARI) A053644(n)=my(k=1);while(k<=n,k<<=1);k>>1;
%o forprime(p=2,1e3,if(isprime(k=4*A053644(p)+p),print1(k", "))) \\ _Charles R Greathouse IV_, May 27 2011
%o (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
%Y Cf. A004676, A007088, A091932, A080165, A090423, A053644.
%K nonn,easy,base
%O 1,1
%A _Juri-Stepan Gerasimov_, May 27 2011
%E a(4) corrected, a(15)-a(56) added by _Charles R Greathouse IV_, May 27 2011
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