A290098 Characteristic function for A003658 (fundamental discriminants of real quadratic fields).

1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions.

Formula

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/Pi^2 = 0.303963... (A104141). - Amiram Eldar, Jan 14 2024

Mathematica

Block[{nn = 105, t}, t = ConstantArray[0, nn]; ReplacePart[t, Map[# -> 1 &, Select[Range@ nn, NumberFieldDiscriminant@ Sqrt@ # == # &]]]] (* Michael De Vlieger, Aug 23 2017 *)

Prog

(PARI) A290098(n) = isfundamental(n);

Crossrefs

Cf. A003658, A086669, A104141.

Sequence in context: A121262 A181923 A339825 * A102243 A173859 A202108

Adjacent sequences: A290095 A290096 A290097 * A290099 A290100 A290101

Keyword

nonn

Author

Antti Karttunen, Aug 22 2017

Status

approved