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%I #74 May 22 2026 00:52:40
%S 1,3,5,13,31,76,198,520,1380,3741,10129,27837,76805,213610,596911,
%T 1675905,4724994,13368647,37947482,108029690,308345825,882177037,
%U 2529347318,7266270535,20912111193,60284108632,174049197968,503218277350,1456840566871,4222790593589,12254164026373,35598556455398,103518206389389
%N Number of primes p such that 3^(n-1) <= p < 3^n.
%C The n-th term is the number of primes in the half-open interval [3^(n-1), 3^n) where n > 0.
%F a(n) = |{p in primes : 3^(n-1) <= p < 3^n}|.
%F From _Alois P. Heinz_, May 08 2026: (Start)
%F a(n) = A000720(A024023(n)) - A000720(A024023(n-1)).
%F a(n) = A055729(n) - A055729(n-1) for n>=3. (End)
%e a(1) = |{2}| = 1.
%e a(2) = |{3, 5, 7}| = 3.
%e a(3) = |{11, 13, 17, 19, 23}| = 5.
%t Differences[PrimePi[3^Range[0, 33] - 1]] (* _Amiram Eldar_, May 09 2026 *)
%Y Cf. A000040, A000244, A000720, A024023, A055729, A162145, A006879.
%K nonn
%O 1,2
%A _Shahin Saadati_, May 08 2026
%E More terms from _Alois P. Heinz_, May 08 2026