A287018 Primes that can be generated by the concatenation in base 2, in ascending order, of two consecutive integers read in base 10.
11, 37, 137, 239, 661, 727, 859, 991, 2081, 2341, 2731, 2861, 3121, 3251, 3511, 9547, 10321, 10837, 11353, 13159, 13417, 13933, 14449, 15739, 34439, 40093, 43177, 43691, 45233, 46261, 60139, 61681, 63737, 135433, 138511, 139537, 144667, 146719, 151849, 154927
Offset: 1
Examples
2 and 3 in base 2 are 10 and 11 and concat(10,11) = 1011 is 11 in base 10. 4 and 5 in base 2 are 100 and 101 and concat(100,101) = 100101 is 37 in base 10.
Programs
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Maple
with(numtheory): P:= proc(q) local a,b,c,n; a:=convert(q+1,binary,decimal); b:=convert(q,binary,decimal); c:=convert(b*10^(ilog10(a)+1)+a,decimal,binary); if isprime(c) then c; fi; end: seq(P(i),i=1..1000);
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Mathematica
Select[Map[FromDigits[Apply[Join, IntegerDigits[#, 2]], 2] &, Partition[Range@ 320, 2, 1]], PrimeQ] (* Michael De Vlieger, May 18 2017 *)
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PARI
lista(nn) = {for (n=1, nn, if (isprime(p=fromdigits(Vec(concat(binary(n), binary(n+1))), 2)), print1(p, ", ")));} \\ Michel Marcus, May 20 2017