A138241 Number of squares of primes between cubes of successive primes.

2, 2, 2, 4, 3, 5, 3, 7, 7, 3, 9, 7, 5, 6, 10, 11, 4, 10, 7, 6, 12, 7, 13, 16, 8, 5, 10, 4, 8, 29, 13, 13, 7, 21, 3, 14, 16, 12, 13, 18, 4, 22, 6, 14, 7, 29, 31, 11, 5, 12, 18, 7, 27, 17, 19, 15, 6, 17, 12, 6, 31, 36, 17, 7, 9, 44, 19, 34, 4, 13, 20, 29, 15, 19, 11, 23, 27, 11, 27, 31, 7, 37

Offset

1,1

Comments

Or, number of terms in A001248 between A030078(n) and A030078(n+1).

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Example

First two cubes of primes: between p(1)^3=8 and p(2)^3=27 there are exactly two squares of primes, 9 and 25, hence a(1)=2. Similarly, between p(2)^3=27 and p(3)^3=125, there are exactly 2 squares of primes, 49 and121, hence a(2)=2. (Typo corrected Jul 01 2008.)
{n,p(n)^3,p(n+1)^3}, (squares of primes)}, a(n)}
n=1: {8,27}, {9,25}, a(n)=2
n=2: {27,125}, {49,121}, a(n)=2
n=3: {125,343}, {169,289}, a(n)=2
n=4: {343,1331}, {361,529,841,961}, a(n)=4
n=5: {1331,2197}, {1369,1681,1849}, a(n)=3
n=6: {2197,4913}, {2209,2809,3481,3721,4489}, a(n)=5
n=7: {4913,6859}, {5041,5329,6241}, a(n)=3
n=8: {6859,12167}, {6889,7921,9409,10201,10609,11449,11881}, a(n)=7
n=9: {12167,24389}, {12769,16129,17161,18769,19321,22201,22801},a(n)=7
n=10: {24389,29791}, {24649,26569,27889}, a(n)=3.

Mathematica

Table[PrimePi[Sqrt[Prime[n + 1]]^3] - PrimePi[Sqrt[Prime[n]]^3], {n, 1, 100}] (* Vincenzo Librandi, Feb 20 2018 *)

Prog

(PARI) A138241(n) = primepi(sqrt(prime(n+1)^3)) - primepi(sqrt(prime(n)^3)) \\ Michael B. Porter, Dec 18 2009

Crossrefs

Cf. A001248 (Squares of primes), A030078 (Cubes of primes).

Sequence in context: A031437 A282561 A237598 * A234615 A029145 A238999

Adjacent sequences: A138238 A138239 A138240 * A138242 A138243 A138244

Keyword

nonn

Author

Zak Seidov, May 17 2008

Status

approved