0,2

Discriminants of imaginary quadratic fields with D=0,1 mod 4, D<0 (sequence gives -D).

n such that Langford-Skolem problem has a solution - see A014552.

A014494(n) = A000217(a(n)); complement of A042963. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 04 2004

Also called skew amenable numbers; a number n is skew amenable if there exist a set {a(i)} of integers satisfying the relations n = sum_(1,n) a(i) = -product_(1,n) a(i). Thus we have 8=1+1+1+1+1+1-2+4=-(1*1*1*1*1*1*(-2)*4). - Lekraj Beedassy (blekraj(AT)yahoo.com), Jan 07 2005

A139131(a(n)) = A078636(a(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 10 2008

Possible nonpositive discriminants of quadratic equation a*x^2+b*x+c or discrminants of binary quadratic forms a*x^2+b*x*y+c^y^2 - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008

Contribution from Rick L. Shepherd (rshepherd2(AT)hotmail.com), Oct 29 2008: (Start)

Also, disregarding the 0 term, positive integers m such that, equivalently,

(i) +-1 +-2 +-... +-m is even for all choices of signs,

(ii) +-1 +-2 +-... +-m = 0 for some choices of signs,

(iii) for all -m <= k <= m, k = +-1 +-2 +-... +-(k-1) +-(k+1) +-(k+2) +-... +-m for at least one choice of signs. (End)

H. Cohen, Course in Computational Alg. No. Theory, Springer, 1993, pp. 514-5.

A. Scholz and B. Schoeneberg, Einfuehrung in die Zahlentheorie, 5. Aufl., de Gruyter, Berlin, New York, 1973, p. 108.

S. F. Barger, Solution to problem 10454, "Amenable Numbers", Amer. Math. Monthly Vol. 105 No. 4 April 1998 MAA Washington DC.

S. R. Finch, Class number theory

a(n) = (n+1)*2 + 1 - n mod 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 21 2003

a(n) = Sum{k=1..n, 2 - (-1)^k} - William A. Tedeschi (fynmun(AT)hotmail.com), Mar 20 2008

a(n)=a(n-1)+a(n-2)-a(n-3). G.f.: x*(3+x)/( (1+x)* (x-1)^2 ). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 25 2009]

a(n) = 2*n + (n mod 2) [From Paolo Valzasina (p.valzasina(AT)gmail.com), Nov 24 2009]

a(n)=4*n-a(n-1)-5 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 22 2009]

For n=2, a(2)=4*2-0-5=3; n=3, a(3)=4*3-3-5=4; n=4, a(4)=4*4-4-5=7 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 22 2009]

aa = {}; Do[Do[Do[d = b^2 - 4 a c; If[d <= 0, AppendTo[aa, -d]], {a, 0, 50}], {b, 0, 50}], {c, 0, 50}]; Union[aa] - Artur Jasinski (grafix(AT)csl.pl), Apr 28 2008

Cf. A079896.

Sequence in context: A032788 A070874 A154708 this_sequence A026444 A003171 A028970

Adjacent sequences: A014598 A014599 A014600 this_sequence A014602 A014603 A014604

nonn,easy,new

Eric Rains (rains(AT)caltech.edu)