cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A269451 The first of 50 consecutive positive integers the sum of the squares of which is a square.

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%I A269451 #19 Oct 22 2016 10:37:33
%S A269451 7,28,44,67,87,124,168,287,379,512,628,843,1099,1792,2328,3103,3779,
%T A269451 5032,6524,10563,13687,18204,22144,29447,38143,61684,79892,106219,
%U A269451 129183,171748,222432,359639,465763,619208,753052,1001139,1296547,2096248,2714784
%N A269451 The first of 50 consecutive positive integers the sum of the squares of which is a square.
%C A269451 Positive integers y in the solutions to 2*x^2-100*y^2-4900*y-80850 = 0.
%C A269451 Numbers n such that 40425 + 2450*n + 50*n^2 is a square. - _Harvey P. Dale_, Oct 22 2016
%H A269451 Colin Barker, <a href="/A269451/b269451.txt">Table of n, a(n) for n = 1..1000</a>
%H A269451 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,6,-6,0,0,0,0,-1,1).
%F A269451 G.f.: x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)).
%e A269451 7 is in the sequence because sum(k=7, 56, k^2) = 60025 = 245^2.
%t A269451 Select[Range[3*10^6],IntegerQ[Sqrt[40425+2450#+50#^2]]&] (* or *) LinearRecurrence[ {1,0,0,0,0,6,-6,0,0,0,0,-1,1},{7,28,44,67,87,124,168,287,379,512,628,843,1099},40] (* _Harvey P. Dale_, Oct 22 2016 *)
%o A269451 (PARI) Vec(x*(7+21*x+16*x^2+23*x^3+20*x^4+37*x^5+2*x^6-7*x^7-4*x^8-5*x^9-4*x^10-7*x^11-x^12) / ((1-x)*(1+2*x^3-x^6)*(1-2*x^3-x^6)) + O(x^40))
%Y A269451 Cf. A001032, A001652, A094196, A106521, A257781, A269447, A269448, A269449.
%K A269451 nonn,easy,less
%O A269451 1,1
%A A269451 _Colin Barker_, Feb 27 2016