Template:Sequence of the Day for June 1

Intended for: June 1, 2014

Timetable

• First draft entered by Charles R Greathouse IV on May 31, 2013 ✓
• Draft to be reviewed by April 1, 2014
• Draft to be approved by May 1, 2014

Yesterday's SOTD * Tomorrow's SOTD

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A118905: Sum of legs of Pythagorean triangles (without multiple entries).

{ 7, 14, 17, 21, 23, 28, 31, 34, 35, 41, 42, 46, 47, 49, 51, 56, 62, 63, 68, 69, 70, 71, 73, ... }

Are these just the positive multiples of A001132? Richard Choulet comments:

A001132 is exactly formed by the prime numbers of A118905: in fact at first every prime p of A118905 is p = u^2 - v^2 + 2uv, with for example u odd and v even so that p - 1 = 4u'(u' + 1) + 4v'(2u' + 1 - v') when u = 2u' + 1 and v = 2v'. u'(u' + 1) is even and v'(2u' + 1 - v') is always even. At second hand if p = 8k +- 1, p has the shape x^2 - 2y^2; letting u = x - y and v = y, comes p = (x - y)^2 - y^2 + 2(x - y)y = u^2 - v^2 + 2uv so p is a sum of the two legs of a Pythagorean triangle.