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A243427 Floored (rational) values of sqrt(xy) such that sqrt(x) + sqrt(y) = sqrt(xy). 0

%I

%S 4,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,

%U 51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66

%N Floored (rational) values of sqrt(xy) such that sqrt(x) + sqrt(y) = sqrt(xy).

%C (n + 1)^2/n = (n + 2 + 1/n) so for n>1 yields n+2 under the floor operation.

%C Consider sqrt(x) + sqrt(y) = sqrt(xy). If we let y=d^2*x, then the LHS becomes (1+d)sqrt(x) and the RHS becomes dx. Divide both sides by sqrt(x), take the d from the RHS to the LHS and square giving x=((1+d)/d)^2, and so y is (1+d)^2 and the original RHS is now (1+d)^2/d. This sequence is concerned with d being an integer.

%C Has solutions for all x<>1.

%F a(n) = floor((n + 1)^2/n).

%F a(n) = n + 2 for n>1.

%e sqrt(4) + sqrt(4) = 4 = sqrt(16).

%e sqrt(9/4) + sqrt(9) = 4.5 = sqrt(81/4).

%o (JavaScript)

%o for (i = 1; i < 150; i++) {

%o document.write(Math.floor((i + 1) * (i + 1)/i) + ", ");

%o }

%K nonn,easy

%O 1,1

%A _Jon Perry_, Jun 05 2014

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Last modified June 27 10:04 EDT 2022. Contains 354896 sequences. (Running on oeis4.)