First 11 values of A121387 coincide with apparently unrelated new seq
Jonathan Post
jvospost3 at gmail.com
Wed Jun 20 07:09:00 CEST 2007
Here's a strange coiuncidence that I hope someone can complain.
I started a new seq that might well be labeled "less" as it seems
arbitrary. But it looked like an existing seq for 11 values before
differing.
Semiprimes which are the hypotenuses of primitive Pythagorean triples.
A001358 INTERSECTION A020882
If I list these with multiplicity (multiple primitive triples shown)
this begins:
n a(n) triple(s)
1 25 (7,24,25)
2 65 (16, 63, 65)
3 85 (13, 84, 85)
4 85 (36, 77, 85)
5 145 (77, 144, 145)
6 145 (24, 143, 145)
7 169 (119, 120, 169)
8 185 (57, 176, 185)
9 185 (104, 153, 185)
10 205 (133, 156, 205)
11 205 (84, 187, 205)
12 221 (21, 220, 221)
13 221 (140, 171, 221)
14 265 (23, 264, 265)
15 265 (96, 247, 265)
16 289 (161, 240, 289)
17 305 (207, 224, 305)
18 305 (136, 273, 305)
19 365 (27, 364, 365)
20 365 (76, 357, 365)
If I give the set of values (without multiplicity) it begins:
25, 65, 85, 145, 169, 185, 205, 221, 265, 289, 305, 365
The first 11 values are the same as the apparently unrelated A121387
which begins:
25, 65, 85, 145, 169, 185, 205, 221, 265, 289, 305, 329, 365, 377,
445, 481, 485, 493
but the 329 which is a(12) of A121387 is a semiprime (7 * 47) but is
NOT a primitive Pythagorean hypotenuse.
Just when I was about to make a conjecture, the Law of Small Numbers kicked in!
Any ideas?
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