|
Search: id:A050795
|
|
|
| A050795 |
|
Numbers n such that n^2 - 1 is expressible as the sum of two nonzero squares in at least one way. |
|
+0
8
|
|
| 3, 9, 17, 19, 33, 35, 51, 73, 81, 99, 105, 129, 145, 147, 161, 163, 179, 195, 201, 233, 243, 273, 289, 291, 297, 339, 361, 387, 393, 451, 465, 467, 483, 489, 513, 521, 577, 579, 585, 611, 627, 649, 675, 721, 723, 739, 777, 801, 809, 819, 849, 883, 899, 915
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
Analogous solutions exist for the sum of two identical squares z^2-1 = 2.r^2 (e.g. 99^2-1 = 2.70^2). Values of 'z' are the terms in sequence A001541, values of 'r' are the terms in sequence A001542.
Looking at a^2 + b^2 = c^2 - 1 modulo 4, we must have a and b even and c odd. Taking a = 2u, b = 2v and c = 2w - 1 and simplifying, we get u^2 + v^2 = w(w+1) - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 19 2008
|
|
LINKS
|
Index entries for sequences related to sums of squares
|
|
FORMULA
|
a(n) = 2*A140612(n) + 1. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), May 19 2008
|
|
EXAMPLE
|
E.g. 51^2 - 1 = 10^2 + 50^2 = 22^2 + 46^2 = 34^2 + 38^2.
|
|
CROSSREFS
|
Cf. A050796, A050797, A001541, A001542, A001333.
Cf. A140612, A002378.
Sequence in context: A145796 A056403 A106676 this_sequence A050797 A103967 A032400
Adjacent sequences: A050792 A050793 A050794 this_sequence A050796 A050797 A050798
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Patrick De Geest (pdg(AT)worldofnumbers.com), Sep 15 1999.
|
|
|
Search completed in 0.002 seconds
|
