A033843 Number of twin primes < 2^n.

0, 1, 2, 3, 5, 7, 10, 17, 24, 36, 62, 107, 177, 290, 505, 860, 1526, 2679, 4750, 8535, 15500, 27995, 50638, 92246, 168617, 309561, 571313, 1056281, 1961080, 3650557, 6810670, 12739574, 23878645, 44849427, 84384508, 159082253, 300424743, 568237005, 1076431099, 2042054332, 3879202049

Offset: 1

Author

Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998

Keywords

• nonn
• hard

Comments

For n=2 only the lower member of the pair [3,5] is < 2^n. - Hugo Pfoertner, Feb 07 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..53
• Index entries for sequences related to numbers of primes in various ranges.

Crossrefs

Cf. A007053, A007508.

Partial sums of A095017.

Programs

Mathematica

a[n_] := Count[Range[2^n], ?(And @@ PrimeQ[# + {-1, 1}] &)]; Array[a, 20] (* _Amiram Eldar, Jul 18 2025 *)

Extensions

a(38) from Alex Ratushnyak, Jun 07 2013

a(39)-a(41) from Hugo Pfoertner, Feb 07 2024