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Search: id:A143697
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| A143697 |
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Least square k^2 such that n^2-k^2 = p*q with p and q odd primes and p<q for n>= 4. |
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3
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| 1, 4, 1, 16, 9, 4, 9, 36, 1, 36, 9, 4, 9, 36, 1, 144, 9, 4, 81, 36, 25, 36, 9, 16, 81, 144, 1, 144, 81, 16, 9, 36, 25, 36, 81, 4, 9, 144, 1, 576, 9, 4, 225, 36, 25, 144, 9, 64, 81, 36, 49, 144
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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The product p*q is the sum of p consecutive odd numbers with 2*n-1 the greatest.
For n=4 p*q=3*5=15, 15=7+5+3
For n=5 p*q=3*7=21, 21=9+7+5
For n=6 p*q=5*7=35, 35=11+9+7+5+3
For n=7 p*q=3*11=33, 33=13+11+9
k^2 is the sum of the k first consecutive odd numbers
p=n-k and q=n+k
Assuming a strong version of the Goldbach conjecture, every term exists and we have a(n)=A082467(n)^2, p(n)=A078587(n) and q(n)=A078496(n). [From T. D. Noe (noe(AT)sspectra.com), Jan 22 2009]
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LINKS
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P. CAMI, Table of n, a(n) for n = 4..60000
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EXAMPLE
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4*4-1=3*5 p=3 q=5
5*5-4=3*7 p=3 q=7
6*6-1=5*7 p=5 q=7
7*7-16=3*11 p=3 q=11
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CROSSREFS
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Cf. A078587, A078496.
Sequence in context: A038231 A104855 A143496 this_sequence A117438 A075499 A099394
Adjacent sequences: A143694 A143695 A143696 this_sequence A143698 A143699 A143700
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KEYWORD
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nonn
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AUTHOR
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Pierre CAMI (pierrecami(AT)tele2.fr), Aug 29 2008
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