[seqfan] Erroneous comment in A096033
Andrew Weimholt
andrew.weimholt at gmail.com
Tue Sep 7 23:47:41 CEST 2010
A096033 is
Difference between leg and hypotenuse in primitive Pythagorean triangles.
1, 2, 8, 9, 18, 25, 32, 49, 50, 72, 81, 98, 121, 128, 162, 169, 200,
225, 242, 288, 289, 338, 361, 392, 441, 450, 512, 529, 578, 625, 648,
722, 729, 800, 841, 882, 961, 968, 1058, 1089, 1152, 1225, 1250, 1352,
1369, 1458, 1521, 1568, 1681, 1682, 1800, 1849
The following comment is completely wrong:
This sequence contains all numbers containing 2 to an odd power or
some other prime to an odd power. - Edoardo Gueglio
(egueglio(AT)yahoo.it), Aug 28 2007
The sequence is simply the odd squares and the halves of the even squares.
Consequently, the sequence contains all odd powers of 2, but not all numbers
containing odd powers of 2 as suggested by Edoardo's comment. The sequence
also does not contain any odd powers of other primes. As all the terms
are squares or
halves of squares, the powers of any odd prime factors must be even.
Andrew
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