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

1,1

Links

Table of n, a(n) for n=1..42.

Example

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.

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);

Mathematica

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

Prog

(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

Crossrefs

Cf. A000040, A052089, A287018.

Subsequence of primes of A277351.

Sequence in context: A304782 A184435 A112266 * A215169 A072468 A148430

Adjacent sequences: A287016 A287017 A287018 * A287020 A287021 A287022

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 18 2017

Extensions

First term added by Michel Marcus, May 23 2017

Status

approved