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 A274545 Values of k such that 5*k-1 and 10*k-1 are both perfect squares. 2

%I

%S 1,29,33293,1130977,1305146305,44336554445,51164345409437,

%T 1738081606216033,2005744667435597089,68136275082544365341,

%U 78629202401645931667661,2671078254047822603875969,3082421990543579145800043553,104711609647046466634601365517

%N Values of k such that 5*k-1 and 10*k-1 are both perfect squares.

%C Intersection of A062317 and A220082.

%H Colin Barker, <a href="/A274545/b274545.txt">Table of n, a(n) for n = 1..400</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,39202,-39202,-1,1).

%F a(n) = a(n-1) + 39202*a(n-2) - 39202*a(n-3) - a(n-4) + a(n-5) for n>5.

%F G.f.: x*(1 + 28*x - 5938*x^2 + 28*x^3 + x^4)/((1 - x)*(1 - 198*x + x^2)*(1 + 198*x + x^2)).

%e 29 is in the sequence because 5*29-1 = 144 = 12^2, and 10*29-1 = 289 = 17^2.

%t Rest@ CoefficientList[Series[x (1 + 28 x- 5938 x^2 + 28 x^3 + x^4) / ((1 - x) (1 - 198 x + x^2) (1 + 198 x + x^2)), {x, 0, 17}], x] (* _Michael De Vlieger_, Jun 27 2016 *)

%o (PARI) Vec(x*(1+x)*(1-6*x+x^2)/((1-x)*(1-34*x+x^2)*(1+x+x^2)) + O(x^20))

%o (PARI) isok(n) = issquare(5*n-1) && issquare(10*n-1); \\ _Michel Marcus_, Jun 28 2016

%Y Cf. A062317, A220082, A274544.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jun 27 2016

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Last modified January 27 14:07 EST 2021. Contains 340467 sequences. (Running on oeis4.)