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A127690
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a(1)=3; for n>1, a(n) is least number such a(1)^2+...+a(n)^2 is a square and is equal to (1+a(n))^2.
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2
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OFFSET
| 1,1
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REFERENCES
| Sierpinski W., 1959 Toria Liczb (=Theory of Numbers) Part II. Monografie Matematyczne Tom 38. PWN Warszawa, pp. 1-487 (p.76).
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FORMULA
| Conjecture: a(n)=A053630(n-1)-1 for n>=2. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2007
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EXAMPLE
| a(2)=4 because (3^2+4^2=5^2) and (4+1=5), a(3)=12 because (3^2+4^2+12^2=13^2) and (12+1=13) a(5)= 3612 because (3^2+4^2+12^2+84^2+3612^2=3613^2) and (3612+1=3613) etc.
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MATHEMATICA
| a = {3}; For[k = 1 + a[[Length[a]]], Length[a] < 5, While[ ! ((IntegerQ[Sqrt[(k)^2 + Sum[(a[[t]])^2, {t, 1, Length[a]}]]]) && (Sqrt[(k)^2 + Sum[(a[[t]])^2, {t, 1, Length[a]}]] == k + 1)), k++ ]; AppendTo[a, k]]; a
a = {3}; For[k = 1 + a[[Length[a]]], Length[a] < 12, s2 = Plus @@ (a^2); t = Reduce[{y^2 + s2 == (y + 1)^2}, y, Integers]; t = t /. {Equal -> Rule}; k = y /. t; AppendTo[a, k]]; a (* Daniel Huber *)
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CROSSREFS
| Cf. A018930, A127689, A127691.
Sequence in context: A059792 A018930 A127689 * A092417 A071543 A127611
Adjacent sequences: A127687 A127688 A127689 * A127691 A127692 A127693
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Jan 23 2007, Jan 29 2007
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