A256468 Number of primes between prime(n)^2 and prime(n)*prime(n+1).

1, 2, 2, 6, 4, 8, 5, 12, 22, 8, 27, 21, 11, 23, 38, 36, 16, 43, 31, 15, 52, 36, 52, 75, 45, 22, 42, 19, 48, 160, 47, 81, 22, 141, 26, 90, 89, 65, 102, 96, 40, 180, 40, 73, 38, 227, 227, 85, 44, 85, 129, 43, 216, 133, 140, 137, 45, 147, 105, 46, 260, 354, 115, 52, 108, 386, 165, 283, 64

Offset: 1

Author

Antti Karttunen, Mar 30 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6542
• A. Karttunen, Ratio a(n)/A256469(n) plotted with OEIS Plot2-script
• A. Karttunen, Ratio a(n)/A050216(n) plotted with OEIS Plot2-script

Crossrefs

One less than A256447.

Cf. A050216, A256469, A256470.

Programs

Mathematica

Table[Abs@ Subtract[PrimePi[Prime[n]^2], PrimePi[Prime[n] Prime[n + 1]]], {n, 69}] (* Michael De Vlieger, Mar 30 2015 *)
PrimePi[Times@@#]-PrimePi[#[[1]]^2]&/@Partition[Prime[Range[70]],2,1] (* Harvey P. Dale, Mar 31 2025 *)

PARI

allocatemem(234567890);
default(primelimit,4294965247);
A256468(n) = (primepi(prime(n)*prime(n+1)) - primepi(prime(n)^2));
for(n=1, 6542, write("b256468.txt", n, " ", A256468(n)));

Scheme

(define (A256468 n) (let* ((p (A000040 n)) (p2 (* p p))) (let loop ((s 0) (k (* p (A000040 (+ 1 n))))) (cond ((= k p2) s) (else (loop (+ s (if (prime? k) 1 0)) (- k 1)))))))

Formula

a(n) = A256447(n)-1.

a(n) = A050216(n) - A256469(n).

a(n) = A256469(n) - A256470(n).