This site is supported by donations to The OEIS Foundation.

7-rough numbers

From OeisWiki
Jump to: navigation, search


This article page is a stub, please help by expanding it.


Least prime factor ≥ 7.

Sequences

A007775 7-rough numbers: positive integers that have no prime factors less than 7.

{1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 119, 121, 127, 131, 133, 137, 139, 143, 149, ...}

In every block of 30 consecutive integers, there are exactly eight 7-rough numbers, so this sequence has natural density 8/30 = 4/15 = 0.2666....

This sequence corresponds to a prime sieve consisting of 8 candidates
[30 k + 1, 30 k + 7, 30 k + 11, 30 k + 13, 30 k + 17, 30 k + 19, 30 k + 23, 30 k + 29]
in 30 non-negative whole numbers
[30 k, 30 k + 29]
. Multiples of 2, 3, or 5 are excluded. Bit 0 in this sieve represents 1, bit 1 represents 7, ..., bit 7 represents 29. The first composite numbers in the sequence are 7 × 7 = 49, 7 × 11 = 77, 7 × 13 = 91, 7 × 17 = 119, 11 × 11 = 121, 11 × 13 = 143, and so on.

See also