login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A127924 One-seventh of the difference of squares of legs of primitive Pythagorean triangles, neither of which is a multiple of 7. 0
1, 17, 23, 103, 137, 199, 217, 497, 601, 697, 799, 1343, 1457, 1679, 1799, 2737, 2839, 2921, 3199, 3337, 3503, 3503, 3937, 3961, 3977, 4183, 4577, 4657, 5543, 6103, 6463, 7399, 7663, 8143, 8977, 9143, 9881, 10097, 10577, 10897, 10943, 11543, 13703, 13817 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If 7 divides neither m nor n, then from Fermat's little theorem, 7 divides M^3 - N^3 =( alpha)*Q, where alpha= M - N and Q=M^2 + M*N + N^2, with M=m^2, N=n^2; Here we have (alpha)^2 + (beta)^2 = (gamma)^2, with (beta)^2 =4*M*N and (gamma)^2=M + N. Thus if further 7 does not divide alpha, then 7 divides Q - 7M*N=(M - N)^2 - 4*M*N=(alpha)^2 - (beta)^2, so that 7 always divides (alpha)*(beta)*(alpha^2 - beta^2). In a primitive Pythagorean triangle, 7 divides one of the legs or their sum or their difference.

3503 appears twice in the sequence for (a,b)=(52,165) and (1748,1755). - Chandler

LINKS

Table of n, a(n) for n=1..44.

CROSSREFS

Cf. A127923.

Sequence in context: A260179 A100473 A060252 * A250640 A108260 A062628

Adjacent sequences:  A127921 A127922 A127923 * A127925 A127926 A127927

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Feb 06 2007

EXTENSIONS

Extended by Ray Chandler, Apr 11 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 16 04:23 EDT 2019. Contains 325064 sequences. (Running on oeis4.)