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A145906
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Concerning hypotenuses of triangles such that the sum of the two legs is a perfect square.
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2
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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(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.
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CROSSREFS
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KEYWORD
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nonn,uned
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AUTHOR
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STATUS
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approved
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