A387646 Characteristic function of A000537.

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

Offset

0

Comments

The n-th 1 is followed by n^3 - 1 zeros.

Characteristic function of triangular numbers squared.

Links

Table of n, a(n) for n=0..86.

Chai Wah Wu, Algorithms for Complementary Sequences, Integers (2025) Vol. 25, Art. No. A95. See p. 24.

Formula

a(n) = 1 if n is the sum of the first floor((4n)^(1/4)) cubes and a(n) = 0 otherwise.

Mathematica

a[n_]:=Boole[IntegerQ[(Sqrt[1+8Sqrt[n]]-1)/2]]; Array[a, 87, 0] (* Stefano Spezia, Sep 08 2025 *)

Prog

(Python)
from math import isqrt
def A387646(n): return int(n==((m:=isqrt(isqrt(n<<2)))*(m+1)>>1)**2)

Crossrefs

Cf. A000537,

Cf. characteristic functions of sum of first n k-th powers: (k=1) A010054, (k=2) A253903, (k=3) this sequence.

Sequence in context: A016335 A016373 A281815 * A353633 A393068 A205988

Adjacent sequences: A387643 A387644 A387645 * A387647 A387648 A387649

Keyword

nonn,easy

Author

Chai Wah Wu, Sep 04 2025

Status

approved