OFFSET
1,1
COMMENTS
Sequence lists square roots of square terms of A273318.
Numbers n such that (n+k-1)^2 is the sum of two nonzero squares in exactly k ways for all k = 1, 2, 3 are 11998, 40748, 54248, ...
EXAMPLE
3444 is a term because;
3444^2 = 756^2 + 3360^2.
3444^2 + 1 = 681^2 + 3376^2 = 1^2 + 3444^2.
3444^2 + 2 = 83^2 + 3443^2 = 1547^2 + 3077^2 = 1987^2 + 2813^2.
MATHEMATICA
nR[n_] := (SquaresR[2, n] + Plus @@ Pick[{-4, 4}, IntegerQ /@ Sqrt[{n, n/2} ]])/8; Select[ Range[ 10^5], nR[#^2] == 1 && nR[#^2 + 1] == 2 && nR[#^2 + 2] == 3 &] (* Giovanni Resta, May 20 2016 *)
PROG
(PARI) is(n, k) = {nb = 0; lim = sqrtint(n); for (x=1, lim, if ((n-x^2 >= x^2) && issquare(n-x^2), nb++); ); nb == k; }
isok(n) = is(n^2, 1) && is(n^2+1, 2) && is(n^2+2, 3);
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, May 20 2016
EXTENSIONS
a(7)-a(33) from Giovanni Resta, May 20 2016
STATUS
approved