A073799 -id:A073799 - cp's OEIS frontend

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

Labos Elemer, Aug 14 2002

nonn

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).

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

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

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

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 *)

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

Edited by Dean Hickerson, Aug 15 2002

A073800 Remainder of division 2^n/c(n), where c(n)=A002808(n), the n-th composite.

Original entry on oeis.org

2, 4, 0, 7, 2, 4, 2, 1, 0, 16, 8, 1, 8, 16, 18, 16, 14, 8, 8, 0, 2, 30, 18, 28, 14, 4, 8, 16, 28, 19, 6, 16, 29, 34, 8, 40, 2, 14, 8, 16, 14, 4, 8, 4, 0, 49, 62, 52, 32, 4, 8, 46, 17, 20, 65, 22, 32, 16, 62, 64, 32, 64, 41, 16, 32, 64, 48, 70, 48, 24, 32, 22, 74, 84, 8, 16, 32, 52

Offset: 1

Labos Elemer, Aug 12 2002

nonn

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Cf. A000079, A002808, A015910, A062173, A064367, A073797, A073798, A073799.

Table[Mod[2^j, FixedPoint[j+PrimePi[ # ]+1&, j]], {j, 1, 128}]
Module[{c=Select[Range[200],CompositeQ],len},len=Length[c];Table[ PowerMod[ 2,n,c[[n]]],{n,len}]] (* Harvey P. Dale, Mar 03 2018 *)

cp's OEIS Frontend

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

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