A061273 -id:A061273 - cp's OEIS frontend

A061274 Number of primes between Pi^(n-1) and Pi^n.

2, 2, 7, 14, 37, 100, 271, 742, 2054, 5813, 16507, 47501, 137306, 399685, 1169789, 3438915, 10153559, 30083443, 89426830, 266598341, 796863253, 2387439540, 7168302094, 21565117858, 64993345011, 196202749033, 593205591259, 1796057856430, 5445108651668, 16528162238845

Offset: 1

Amarnath Murthy, Apr 25 2001

nonn

			a(1) = 2 as 2 and 3 are the two primes between 1 and Pi. a(4) = 14 as there are 14 primes between Pi^3 = 31.006... and Pi^4 = 97.409091...

Amiram Eldar, Table of n, a(n) for n = 1..52 (calculated from the b-file at A071973)

Cf. A061273, A071973.

Maple
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See A061273.
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p = q = 0; Do[m = n; q = PrimePi[Pi^n]; Print[q - p]; p = q, {n, 1, 28}]
Differences[PrimePi[Pi^Range[0,27]]] (* Harvey P. Dale, Aug 17 2016 *)

a(n) = A071973(n) - A071973(n-1). - Amiram Eldar, Jun 14 2024

More terms from Winston C. Yang (winston(AT)cs.wisc.edu), May 17 2001
Edited and extended by Robert G. Wilson v, Jun 18 2002
a(28)-a(30) from Amiram Eldar, Jun 14 2024

A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 10, 4, 7, 4, 3, 2, 1, 2, 18, 2, 2, 17, 1, 2, 6, 9, 3, 1, 1, 1, 8, 3, 2, 15, 1, 4, 1, 1, 7, 7, 4, 4, 3, 4, 1, 1, 7, 2, 5, 1, 5, 18, 2, 5, 4, 3, 1, 5, 1, 18, 12, 2, 8, 1, 4, 2, 5, 4, 1, 1, 1, 9, 10

Offset: 1

Omar E. Pol, Aug 23 2007

a(k) corresponds to the k-th term in the isolated prime sequence A007510 or A134797. a(1) corresponds to 23. a(2) corresponds to 37. a(3) corresponds to 47 and 53. - Enrique Navarrete, Jan 28 2017

Lengths of the runs of consecutive integers in A176656. - R. J. Mathar, Feb 19 2017

C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001223, A007510 (isolated primes), A027883, A048614, A048198, A052011, A052012, A061273, A076777, A073784, A082602, A088700, A179067 (clusters of twin primes).

cp's OEIS Frontend

A061274 Number of primes between Pi^(n-1) and Pi^n.

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