A145906 Concerning hypotenuses of triangles such that the sum of the two legs is a perfect square.

9, 19, 27, 33, 57, 51, 51, 73, 89, 83, 107, 99, 139, 129, 137, 123, 129, 187, 187, 163, 177, 171, 209, 257, 201, 233, 267, 227, 251, 337, 243, 321, 313, 307, 297, 289, 291, 387, 411, 363, 347, 393, 339, 379, 369, 363, 417, 401, 393, 491, 499, 473, 593, 449

Offset

0,1

Comments

Last digit is never 5.

Frenicle considers numbers N (apparently the set of A058529 or A120681) and their squares N^2. These have representations N=2*b^2-a^2 = d^2-2*c^2 with d=b+c and N^2 = 2*f^2-e^2 = h^2-2*g^2 with h=f+g. For example N=7 with a=1, b=2, c=1, d=3 and N^2=49 with e=1, f=5, g=4, h=9. The current sequence contains the list of h's.

Apparently the list of N^2 is A089552, the list of a in A143732, the list of b in A147847, the list of e (in different order) in A152910, the list of f (sorted into a different order) in A020882.

Links

Table of n, a(n) for n=0..53.

M. de Frenicle, Methode pour trouver la solutions des problemes par les exclusions, in: Divers ouvrages des mathematiques et de physique par messieurs de l'academie royale des sciences, (1693) pp 1-44.

Example

(a,b,c,d,e,f,g,h) = (1,2,1,3,1,5,4,9) with N=7 or  (1,3,2,5,7,13,6,19) with N=17 or (3,4,1,5,7,17,10,27) with N=23 or (1,4,3,7,17,25,8,33) with N=31.

Crossrefs

Cf. A144407

Sequence in context: A350261 A091592 A174372 * A090065 A098791 A041156

Adjacent sequences: A145903 A145904 A145905 * A145907 A145908 A145909

Keyword

nonn,uned

Author

Paul Curtz, Oct 23 2008

Status

approved