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

1,1

Links

Table of n, a(n) for n=1..40.

Example

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.

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);

Mathematica

Select[Map[FromDigits[Apply[Join, IntegerDigits[#, 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), binary(n+1))), 2)), print1(p, ", "))); } \\ Michel Marcus, May 20 2017

Crossrefs

Cf. A000040, A030458, A287019.

Subsequence of primes of A087737.

Sequence in context: A356278 A355630 A306423 * A152094 A227412 A160623

Adjacent sequences: A287015 A287016 A287017 * A287019 A287020 A287021

Keyword

nonn,base,easy

Author

Paolo P. Lava, May 18 2017

Status

approved