A137382 Number of primes between Pi^(prime(n)) and Pi^(prime(n+1)).

7, 51, 371, 25116, 184807, 15161948, 119510273, 10619203228, 8117133311259, 66755371425339, 59943578764218680, 5202903726035784628, 44211655386352360485, 4351545315671679793432

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Apr 09 2008

Keywords

• nonn
• more

Examples

			7 primes between Pi^2 (9.8...) and Pi^3 (31.0...).
51 primes between Pi^3 (31.0...) and Pi^5 (306.0...).
371 primes between Pi^5 (306.0...) and Pi^7 (3020.29...).
		

Crossrefs

Cf. A000796, A061274, A071973.

Programs

Mathematica

Table[PrimePi[Pi^(Prime[n + 1])] - PrimePi[Pi^(Prime[n])], {n, 1, 8}]

Formula

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

Extensions

a(9)-a(14) calculated from the data at A071973 and added by Amiram Eldar, Jun 14 2024