A365767 a(n) is the number of primes between (prime(n))^3 and (prime(n+1))^3.

5, 21, 38, 149, 110, 329, 226, 575, 1250, 521, 1966, 1656, 939, 2127, 3830, 4665, 1768, 5883, 4535, 2387, 8007, 5968, 9965, 15293, 8508, 4457, 9513, 4974, 10458, 42153, 13671, 21959, 7750, 41767, 9007, 28180, 30226, 21322, 33813, 35899, 12506, 66241, 14003, 28809, 14848, 94735

Offset

1,1

Links

Table of n, a(n) for n=1..46.

Formula

a(n) = A038098(A000040(n+1)) - A038098(A000040(n)).

Example

a(2) = 21 because there are 21 primes between prime(2)^3 = 27 and prime(3)^3 = 125.

Maple

A:= [seq(numtheory:-pi(ithprime(i)^3), i=1..30)]:
A[2..-1] - A[1..-2];

Mathematica

PrimePi[#[[2]]]-PrimePi[#[[1]]]&/@Partition[Prime[Range[50]]^3, 2, 1] (* Harvey P. Dale, Oct 23 2025 *)

Crossrefs

First differences of A086688.

Cf. A038098, A050216.

Sequence in context: A341198 A038844 A303521 * A394300 A372518 A147345

Adjacent sequences: A365764 A365765 A365766 * A365768 A365769 A365770

Keyword

nonn

Author

Zak Seidov and Robert Israel, Sep 18 2023

Status

approved