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Primes p such that p-2 and q are primes, where q is concatenation of binary representations of p and p-2: q = p * 2^L + p-2, where L is the length of binary representation of p-2: L=A070939(p-2).
3

%I #8 Feb 25 2018 11:17:02

%S 5,7,31,271,283,433,1291,1321,1429,1489,1951,4723,5503,6091,6133,6553,

%T 6871,16651,16981,17029,17191,17209,17749,17791,18541,18919,19471,

%U 20149,20479,20551,20809,21319,21649,21739,22111,25309,25801,27061,27409,27541,27691,28549,29131

%N Primes p such that p-2 and q are primes, where q is concatenation of binary representations of p and p-2: q = p * 2^L + p-2, where L is the length of binary representation of p-2: L=A070939(p-2).

%H Harvey P. Dale, <a href="/A232237/b232237.txt">Table of n, a(n) for n = 1..1000</a>

%F A232235(n) = a(n) * 2^A070939(a(n)-2) + a(n)-2.

%e 5 is 101 in binary, 3 is 11, and because 10111 = 23d is a prime, 5 is in the sequence.

%t Select[Partition[Prime[Range[3200]],2,1],#[[2]]-#[[1]]==2&&PrimeQ[ FromDigits[ Join[IntegerDigits[#[[2]],2],IntegerDigits[#[[1]],2]],2]]&][[All,2]] (* _Harvey P. Dale_, Feb 25 2018 *)

%Y Cf. A000040, A070939, A232235.

%K nonn,base,less

%O 1,1

%A _Alex Ratushnyak_, Nov 20 2013