Template:Sequence of the Day for April 7

Intended for: April 7, 2013

Timetable

• First draft entered by Alonso del Arte on January 24, 2012 ✓
• Draft reviewed by Alonso del Arte on December 17, 2012 ✓ (and by Daniel Forgues on April 10, 2016 ✓, April 6, 2018 ✓)
• Draft to be approved by March 7, 2013

Yesterday's SOTD * Tomorrow's SOTD

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A038179: Result of second stage of the sieve of Eratosthenes.

{ 2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, ... }

As you can see, a lot of composites have been culled out: all multiples of 2 and 3 have been culled out, save 2 and 3. After 2 and 3, we are left with all integers of the form

6 k ∓ 1, k   ≥   1

.
Alexander Povolotsky astutely observed that “terms of this sequence [after 3] are equal to the result of the expression

2√  4! (k + 1) + 1

, but only when this expression yields integral values.”