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Search: id:A154708
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| A154708 |
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Numbers a such that b and c exist with b <= a < c and a*(a+1)+b^2=c^2. |
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+0
1
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| 3, 4, 7, 8, 11, 12, 15, 16, 19, 20, 23, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 44, 47, 48, 51, 52, 55, 56, 59, 60, 63, 64, 67, 68, 71, 72, 75, 76, 79, 80, 83, 84, 87, 88, 91, 92, 95, 96, 99, 100, 103
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OFFSET
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1,1
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COMMENT
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Numbers a such that a*(a+1)=c2-b2 with b<=a<c let a(1)=3 then a(2*n)=a(2*n-1)+1 and a(2*n+1)=a(2*n)+3 [From Pierre CAMI (pierre-cami(AT)orange.fr), Jan 15 2009]
Essentially the same as A014601. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2009]
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FORMULA
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a(1)=4; thereafter a(2*n)=a(2*n-1)+3, a(2*n+1)=a(2*n)+1.
a(n)=4*n-a(n-1)-1 (with a(1)=3) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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EXAMPLE
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4*5+4*4=6*6 7*8+5*5=9*9 8*9+7*7=11*11
3*4=4*4-2*2:a(1)=3 4*5=6*6-4*4:a(2)=4 7*6=9*9-5*5:a(3)=7 [From Pierre CAMI (pierre-cami(AT)orange.fr), Jan 15 2009]
For n=2, a(2)=4*2-3-1=4; n=3, a(3)=4*3-4-1=7; n=4, a(4)=4*4-7-1=8 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
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CROSSREFS
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Sequence in context: A153144 A032788 A070874 this_sequence A014601 A026444 A003171
Adjacent sequences: A154705 A154706 A154707 this_sequence A154709 A154710 A154711
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KEYWORD
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nonn,new
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AUTHOR
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Pierre CAMI (pierre-cami(AT)orange.fr), Jan 14 2009, Jan 15 2009
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