OFFSET
1,1
COMMENTS
(n + 1)^2/n = (n + 2 + 1/n) so for n>1 yields n+2 under the floor operation.
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.
Has solutions for all x<>1.
FORMULA
a(n) = floor((n + 1)^2/n).
a(n) = n + 2 for n>1.
EXAMPLE
sqrt(4) + sqrt(4) = 4 = sqrt(16).
sqrt(9/4) + sqrt(9) = 4.5 = sqrt(81/4).
PROG
(JavaScript)
for (i = 1; i < 150; i++) {
document.write(Math.floor((i + 1) * (i + 1)/i) + ", ");
}
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Jun 05 2014
STATUS
approved