A287019 Primes that can be generated by the concatenation in base 2, in descending order, of two consecutive integers read in base 10.
2, 5, 19, 53, 71, 271, 593, 659, 857, 2339, 2729, 3119, 3769, 4159, 8513, 9029, 9803, 10061, 11093, 11351, 11867, 12641, 12899, 13931, 14447, 15737, 16253, 33409, 33923, 36493, 44203, 47287, 51913, 55511, 64763, 133379, 135431, 137483, 141587, 147743, 151847, 158003
Offset: 1
Examples
1 and 2 in base 2 are 1 and 10 and concat(10,1) = 101 is 5 in base 10. 3 and 4 in base 2 are 11 and 100 and concat(100,11) = 10011 is 19 in base 10.
Programs
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Maple
with(numtheory): P:= proc(q) local a,b,c,n; if q=0 then 2 else a:=convert(q+1,binary,decimal); b:=convert(q,binary,decimal); c:=convert(a*10^(ilog10(b)+1)+b,decimal,binary); if isprime(c) then c; fi; fi; end: seq(P(i),i=0..1000);
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Mathematica
Select[Map[FromDigits[Apply[Join, IntegerDigits[Reverse@ #, 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+1), binary(n))), 2)), print1(p, ", ")));} \\ Michel Marcus, May 20 2017
Extensions
First term added by Michel Marcus, May 23 2017