A394209 Number of primes p such that 3^(n-1) <= p < 3^n.

1, 3, 5, 13, 31, 76, 198, 520, 1380, 3741, 10129, 27837, 76805, 213610, 596911, 1675905, 4724994, 13368647, 37947482, 108029690, 308345825, 882177037, 2529347318, 7266270535, 20912111193, 60284108632, 174049197968, 503218277350, 1456840566871, 4222790593589, 12254164026373, 35598556455398, 103518206389389

Offset

1,2

Comments

The n-th term is the number of primes in the half-open interval [3^(n-1), 3^n) where n > 0.

Links

Table of n, a(n) for n=1..33.

Formula

a(n) = |{p in primes : 3^(n-1) <= p < 3^n}|.

From Alois P. Heinz, May 08 2026: (Start)

a(n) = A000720(A024023(n)) - A000720(A024023(n-1)).

a(n) = A055729(n) - A055729(n-1) for n>=3. (End)

Example

a(1) = |{2}| = 1.
a(2) = |{3, 5, 7}| = 3.
a(3) = |{11, 13, 17, 19, 23}| = 5.

Mathematica

Differences[PrimePi[3^Range[0, 33] - 1]] (* Amiram Eldar, May 09 2026 *)

Crossrefs

Cf. A000040, A000244, A000720, A024023, A055729, A162145, A006879.

Sequence in context: A350392 A281874 A135532 * A127600 A262237 A051401

Adjacent sequences: A394206 A394207 A394208 * A394210 A394211 A394212

Keyword

nonn

Author

Shahin Saadati, May 08 2026

Extensions

More terms from Alois P. Heinz, May 08 2026

Status

approved