A287019 - OEIS

%I #15 May 24 2017 09:15:41

%S 2,5,19,53,71,271,593,659,857,2339,2729,3119,3769,4159,8513,9029,9803,

%T 10061,11093,11351,11867,12641,12899,13931,14447,15737,16253,33409,

%U 33923,36493,44203,47287,51913,55511,64763,133379,135431,137483,141587,147743,151847,158003

%N Primes that can be generated by the concatenation in base 2, in descending order, of two consecutive integers read in base 10.

%e 1 and 2 in base 2 are 1 and 10 and concat(10,1) = 101 is 5 in base 10.

%e 3 and 4 in base 2 are 11 and 100 and concat(100,11) = 10011 is 19 in base 10.

%p 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);

%t Select[Map[FromDigits[Apply[Join, IntegerDigits[Reverse@ #, 2]], 2] &, Partition[Range@ 320, 2, 1]], PrimeQ] (* _Michael De Vlieger_, May 18 2017 *)

%o (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

%Y Cf. A000040, A052089, A287018.

%Y Subsequence of primes of A277351.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, May 18 2017

%E First term added by _Michel Marcus_, May 23 2017