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

1,3

Comments

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

Links

Benjamin Chaffin, Table of n, a(n) for n = 1..63 (terms 1..53 from Amiram Eldar)

Index entries for sequences related to numbers of primes in various ranges.

Mathematica

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

Crossrefs

Cf. A007053, A007508.

Partial sums of A095017.

Sequence in context: A182521 A283809 A104622 * A384444 A389621 A397046

Adjacent sequences: A033840 A033841 A033842 * A033844 A033845 A033846

Keyword

nonn,hard

Author

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

Extensions

a(38) from Alex Ratushnyak, Jun 07 2013

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

Status

approved