Template:Sequence of the Day for July 2

Intended for: July 2, 2012

Timetable

• First draft entered by Alonso del Arte on March 5, 2011 based on an almost verbatim copy of a write-up by Daniel Forgues from November 12, 2010. ✓
• Draft reviewed by Alonso del Arte on May 2, 2011 ✓
• Draft approved by Charles R Greathouse IV on July 1, 2011 ✓

Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.

---

A024702:

a (n) = (  pn ) 2  −  1 24

, where

pn , n   ≥   3,

is a prime congruent to

− 1

or

+ 1 (mod 6)

.

{ 1, 2, 5, 7, 12, 15, 22, 35, 40, 57, 70, ... }

For all numbers

p

and

q

congruent to

− 1

or

+ 1 (mod 6)

, we have

p 2  −  q 2

is divisible by 24, so this applies for the unit 1 or any primes

p

and

q

other than 2 or 3. Iterate

p

through all primes other than 2 and 3 and let

q

be 1. This is a subsequence of the generalized pentagonal numbers (see A001318).