A066612 Number of primes between n^n and (n+1)^(n+1).

2, 7, 45, 391, 4376, 60864, 1012186, 19622935, 434351705, 10807060863, 298525056829, 9063891473730, 300004447041493, 10750198453038838, 414596707456493479, 17122019740329088733, 753855850836114017867, 35248703133243910547502

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Example

a(2) = 7 as there are 7 primes between 2^2 (= 4) and 3^3 (= 27) namely 5, 7, 11, 13, 17, 19, and 23.

Mathematica

Table[PrimePi[(k+1)^(k+1)]-PrimePi[k^k], {k, 12}](* Vladimir Joseph Stephan Orlovsky, Nov 30 2010 *)

Crossrefs

Equals first differences of A064151.

Sequence in context: A064606 A331711 A223001 * A098637 A162045 A326878

Adjacent sequences: A066609 A066610 A066611 * A066613 A066614 A066615

Keyword

nonn

Author

Amarnath Murthy, Dec 24 2001

Extensions

Corrected and extended by Robert G. Wilson v, Dec 26 2001

a(12)-a(14) from Donovan Johnson, Oct 14 2010

a(15)-a(18) from Amiram Eldar, Jun 11 2024

Status

approved