A391183 a(n) = 1 if n is a number of the form x^2 + 2*y^2, and otherwise 0.

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

Offset

0

Comments

First differs from A342892 at n = 35.

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Daniel Shanks and Larry P. Schmid, Variations on a theorem of Landau. Part I, Mathematics of Computation, Vol. 20, No. 96 (1966), pp. 551-569.

Index entries for characteristic functions.

Formula

a(n) = [A033715(n) > 0], where [ ] is the Iverson bracket.

a(A002479(n)) = 1 and a(A097700(n)) = 0.

Multiplicative with a(p^e) = 0 if p == 5 or 7 (mod 8) and e is odd, and a(p^e) = 1 otherwise.

Sum_{k=1..n} a(k) ~ b * n / sqrt(log(n)) + O(n/log(n)), where b = A391182 (Shanks and Schmid, 1966).

Mathematica

f[p_, e_] := If[OddQ[e] && Mod[p, 8] > 4, 0, 1]; a[0] = a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100, 0]

Prog

(PARI) a(n) = if(n < 2, 1, my(f = factor(n)); for(i = 1, #f~, if(f[i, 2] % 2 && f[i, 1] % 8 > 4, return(0))); 1);
(Python)
from sympy import factorint
def A391183(n): return int(any(e&1 and p&7>=5 for p, e in factorint(n).items()))^1 # Chai Wah Wu, Dec 04 2025

Crossrefs

Characteristic function of A002479.

Cf. A033715, A097700, A342892, A391182.

Similar sequences: A229062, A353816.

Sequence in context: A114592 A344864 A140653 * A342892 A071036 A071038

Adjacent sequences: A391180 A391181 A391182 * A391184 A391185 A391186

Keyword

nonn,mult,easy

Author

Amiram Eldar, Dec 02 2025

Status

approved