A113971 Number of semiprimes from n to (4/3)*n.

0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 3, 4, 4, 3, 2, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 4, 4, 3, 4, 4, 4, 3, 3, 4, 5, 6, 6, 5, 6, 6, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5

Offset

1,8

Comments

a(n) > 0 for all n > 2. a(n) > 1 for all n > 16. This is a semiprime (A001358) related sequence similar to the prime related Bertrand's postulate [1845] that, for n > 1, there is always at least one prime p such that n < p < 2*n. A060715 is the number of primes between n and 2n. A077463 is the number of primes between n and 2n-2.

Links

Table of n, a(n) for n=1..60.

Eric Weisstein et al., Bertrand's Postulate.

Formula

a(n) = card{S such that S is an element of A001358 and n <= S <= 4*n/3}.

Example

a(1) = 0 because there is no semiprime from 1 through 4/3 = 1.3333...
a(2) = 0 because there is no semiprime from 2 through 8/3 = 2.6666...
a(3) = 1 because there is the semiprime 4 from 3 through 12/3 = 4.

Crossrefs

Cf. A001358, A060715, A077463.

Sequence in context: A321020 A204260 A122923 * A109338 A291191 A273866

Adjacent sequences: A113968 A113969 A113970 * A113972 A113973 A113974

Keyword

easy,nonn

Author

Jonathan Vos Post, Jan 31 2006

Status

approved