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The first of seventeen consecutive positive integers the sum of the squares of which is equal to the sum of the squares of two consecutive positive integers.
4

%I #6 Sep 07 2015 03:31:39

%S 5,23,933,2175,65849,152771,4609041,10692339,322567565,748311503,

%T 22575121053,52371113415,1579935906689,3665229628091,110572938347721,

%U 256513702853499,7738525748434325,17952293970117383,541586229452055573,1256404064205363855

%N The first of seventeen consecutive positive integers the sum of the squares of which is equal to the sum of the squares of two consecutive positive integers.

%C For the first of the corresponding two consecutive positive integers, see A261933.

%H Colin Barker, <a href="/A261935/b261935.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,70,-70,-1,1).

%F G.f.: x*(21*x^4+18*x^3-560*x^2-18*x-5) / ((x-1)*(x^4-70*x^2+1)).

%e 5 is in the sequence because 5^2 + 6^2 + ... + 21^2 = 40^2 + 41^2.

%o (PARI) Vec(x*(21*x^4+18*x^3-560*x^2-18*x-5)/((x-1)*(x^4-70*x^2+1)) + O(x^40))

%Y Cf. A001652, A031138, A261932, A261933, A261934.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Sep 06 2015