A256470 a(n) = A256469(n) - A256468(n).

0, 1, 2, 3, 1, 6, 1, 3, 3, 0, 3, 2, -2, 0, 4, 6, 0, 4, 4, 0, 2, 3, 10, 13, -1, -2, 3, 4, 4, 34, 5, 3, 5, 17, 6, 2, 8, -2, -6, 3, -4, -4, -3, -2, -1, 9, 25, -2, -6, -4, 12, 4, 6, 9, -6, 18, 1, -2, -11, 7, -8, 27, -10, 3, -1, 12, 11, 13, -3, 5, 3, 5, -13, -8, 10, 16, -4, 14, 3, 12, -3, 23, 5, 4, 6, -8, 19, -13, 1, 0

Offset: 1

Author

Antti Karttunen, Mar 30 2015

Keywords

• sign

Comments

a(n) = Difference between the number of primes occurring in range [prime(n)*prime(n+1), prime(n+1)^2] and the number of primes occurring in range [prime(n)^2, prime(n)*prime(n+1)].

In other words, a(n) tells how many more primes there are in the latter part of the range prime(n)^2 .. prime(n+1)^2 (after the geometric mean of its limits), than in its first part (before the geometric mean of its limits).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6541
• A. Karttunen, Sequences A256470 and A050216 compared with OEIS Plot2-script (See also the ratio-plots linked in A256468.)

Crossrefs

Positions of zeros: A256471. Cf. also A256472, A256473.

Positions of nonnegative terms: A256474, negative terms: A256475.

Positions of strictly positive terms: A256476, terms less than or equal to zero: A256477.

Cf. A256449, A256468, A256469.

Programs

Scheme

(define (A256470 n) (- (A256469 n) (A256468 n)))

Formula

a(n) = A256469(n) - A256468(n).

a(n) = 3 - A256449(n).