Define a "super-squared n-tuple" as an n-tuple in which the components are increasing and the sum of the squares of the first k components in the tuple is a perfect square, for all 1<=k<=n. Then this sequence gives the minimal sum of the components of a super-squared n-tuple. - Edward Jiang, Dec 4 2013

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Define a "super-squared n-tuple" as an n-tuple in which the components are increasing and the sum of the squares of the first k components in the tuple is a perfect square, for all 1<=k<=n. Then this sequence gives the minimal sum of the components of a super-squared n-tuple. - Edward Jiang, Dec 4 2013

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Apart from the initial term, the sequence is the same as A053631.

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Sierpinski W., <a href="http://pldml.icm.edu.pl/pldml/details/contents.action?id=bwmeta1.element.dl-catalog-556369c7-b6cc-4a5b-be36-bfc8e0ca7cfa">Elementary theory of numbers</a>, Monografie Matematyczne 42 (1964), Chapter II, p. 63.

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a(1)=3; for n>1, a(n) is least number such that a(1)^2+...+a(n)^2 is a square and is equal to = (1+a(n))^2.

3, 4, 12, 84, 3612, 6526884, 21300113901612, 226847426110843688722000884, 25729877366557343481074291996721923093306518970391612, 331013294649039928396936390888878360035026305412754995683702777533071737279144813617823976263475290370884

Sierpinski W., 1959 Toria Liczb (=Theory of Numbers) Part II. Monografie Matematyczne Tom 38. PWN Warszawa, pp. 1-487 (p.76).

Sierpinski W., <a href="http://pldml.icm.edu.pl/pldml/details/contents.action?id=bwmeta1.element.dl-catalog-556369c7-b6cc-4a5b-be36-bfc8e0ca7cfa">Elementary theory of numbers</a>, Monografie Matematyczne 42 (1964), p. 63.

Conjecture: For n>2, a(n) =A053630 (a(1)^2 + a(2)^2 + ... + a(n-1)^2 - 1 for )/2 = ((a(n>=-1) + 1)^2 - 1)/2. - _R. J. Mathar_, Apr Max Alekseyev_, Nov 23 20072012

a(n) = A053630(n-1)-1 for n>=2. - R. J. Mathar, Apr 23 2007

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_Artur Jasinski (grafix(AT)csl.pl), _, Jan 23 2007, Jan 29 2007