OFFSET
1,1
COMMENTS
Numbers n such that n == 0 (mod 4) or n == 1 (mod 4), but n is not a square.
For an indefinite binary quadratic form over the integers a*x^2 + b*x*y + c*y^2 the discriminant is D = b^2 - 4*a*c > 0; and D not a square is assumed.
Also, a superset of A227453. - Ralf Stephan, Sep 22 2013
For the period length of the continued fraction of sqrt(a(n)) see A267857(n). - Wolfdieter Lang, Feb 18 2016
[I changed the offset to 1, since this is an important list. Many parts of the entry, including the b-file, will need to be changed. - N. J. A. Sloane, Mar 14 2023]
REFERENCES
McMullen, Curtis. "Billiards and Teichmüller curves." Bulletin of the American Mathematical Society, 60:2 (2023), 195-250. See Table C.1.
A. Scholz and B. Schoeneberg, Einführung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, p. 112.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..2001
S. R. Finch, Class number theory
Steven R. Finch, Class number theory [Cached copy, with permission of the author]
FORMULA
a(2*k^2 + 2*k) = 4*(k+1)^2 + 1 for k >= 0. - Gheorghe Coserea, Nov 07 2016
a(2*k^2 + 4*k + 1 + (k+1)*(-1)^k) = (2*k + 3)*(2*k + 3 + (-1)^k) for k >= 0. - Bruno Berselli, Nov 10 2016
MATHEMATICA
Select[ Range[148], (Mod[ #, 4] == 0 || Mod[ #, 4] == 1) && !IntegerQ[ Sqrt[ # ]] & ]
PROG
(PARI) seq(N) = {
my(n = 1, v = vector(N), top = 0);
while (top < N,
if (n%4 < 2 && !issquare(n), v[top++] = n); n++; );
return(v);
};
seq(62) \\ Gheorghe Coserea, Nov 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jan 31 2003
EXTENSIONS
More terms from Robert G. Wilson v, Mar 26 2003
Offset changed to 1 (since this is a list). - N. J. A. Sloane, Mar 14 2023
STATUS
approved