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A274544 Values of k such that 2*k-1 and 5*k-1 are both perfect squares.

%I A274544 #19 Dec 05 2016 08:05:32
%S A274544 1,13,925,18241,1333345,26303005,1922682061,37928914465,2772506198113,
%T A274544 54693468355021,3997952014996381,78867943439025313,
%U A274544 5765044033118582785,113727519745606145821,8313189497804981379085,163995004605220623248065,11987613490790750030057281
%N A274544 Values of k such that 2*k-1 and 5*k-1 are both perfect squares.
%C A274544 Intersection of A001844 and A062317.
%H A274544 Colin Barker, <a href="/A274544/b274544.txt">Table of n, a(n) for n = 1..600</a>
%H A274544 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1442,-1442,-1,1).
%F A274544 a(n) = a(n-1) + 1442*a(n-2) - 1442*a(n-3) - a(n-4) + a(n-5) for n>5.
%F A274544 G.f.: x*(1 + 12*x - 530*x^2 + 12*x^3 + x^4) / ((1 - x)*(1 - 38*x + x^2)*(1 + 38*x + x^2)).
%e A274544 13 is in the sequence because 2*13-1 = 25 = 5^2, and 5*13-1 = 64 = 8^2.
%t A274544 Rest@ CoefficientList[Series[x (1 + 12 x - 530 x^2 + 12 x^3 + x^4)/((1 - x) (1 - 38 x + x^2) (1 + 38 x + x^2)), {x, 0, 17}], x] (* _Michael De Vlieger_, Jun 27 2016 *)
%o A274544 (PARI) Vec(x*(1+12*x-530*x^2+12*x^3+x^4)/((1-x)*(1-38*x+x^2)*(1+38*x+x^2))+ O(x^20))
%o A274544 (PARI) isok(n) = issquare(2*n-1) && issquare(5*n-1); \\ _Michel Marcus_, Jun 28 2016
%Y A274544 Cf. A001844, A062317, A274545.
%K A274544 nonn,easy
%O A274544 1,2
%A A274544 _Colin Barker_, Jun 27 2016