A073798 pi(n) is a power of 2, where pi(n) = A000720(n) is the number of primes <= n.

2, 3, 4, 7, 8, 9, 10, 19, 20, 21, 22, 53, 54, 55, 56, 57, 58, 131, 132, 133, 134, 135, 136, 311, 312, 719, 720, 721, 722, 723, 724, 725, 726, 1619, 1620, 3671, 3672, 8161, 8162, 8163, 8164, 8165, 8166, 17863, 17864, 17865, 17866, 17867, 17868, 17869, 17870

Offset: 1

Author

Labos Elemer, Aug 14 2002

Keywords

• nonn

Comments

The numbers occur in blocks of consecutive integers: 2, 3-4, 7-10, 19-22, ...; the n-th block starts at the 2^n-th prime (A033844) and ends just before the (2^n + 1)-th prime (A051439).

Examples

			10 is in the sequence since pi(10)=4=2^2.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..1103 (n = 1..665 from Ivan Neretin)

Crossrefs

Cf. A000079, A000720, A015910, A073797, A073799.

Programs

Mathematica

pow2[n_] := n==1||(n>1&&IntegerQ[n/2]&&pow2[n/2]); Select[Range[20000], pow2[PrimePi[ # ]]&]
Flatten@Table[Range[p = Prime[2^k], NextPrime[p] - 1], {k, 0, 11}] (* Ivan Neretin, Jan 21 2017 *)

PARI

isok(n) = my(pi = primepi(n)); (pi==1) || (pi==2) || (ispower(primepi(n),,&k) && (k==2)); \\ Michel Marcus, Jan 23 2017

Extensions

Edited by Dean Hickerson, Aug 15 2002