A079495 Numbers k such that the sum of the squares of the digits of k in base 3 is 0 (mod 3).

0, 13, 14, 16, 17, 22, 23, 25, 26, 31, 32, 34, 35, 37, 38, 39, 42, 46, 47, 48, 51, 58, 59, 61, 62, 64, 65, 66, 69, 73, 74, 75, 78, 85, 86, 88, 89, 91, 92, 93, 96, 100, 101, 102, 105, 109, 110, 111, 114, 117, 126, 136, 137, 138, 141, 144, 153, 166, 167, 169, 170, 172, 173

Offset

1,2

Comments

In base 2 this gives the "Evil Numbers" (cf. A001969) and slope 2. One may conjecture that in base b the asymptotic slope will be b and might suspect asymptotic density 1/b for each result (mod b). For nonprime b larger variations occur and "very big" numbers must be considered to believe in the conjecture (1 million or more...). (Related to A006287, here mod b is considered)

Links

Table of n, a(n) for n=1..63.

Example

59 is a member because 59 = 2013_3 and 2^2+0^2+1^2+1^2 = 6 = 0 (mod 3).

Mathematica

Ev = Function[{b, x}, vx = IntegerDigits[x, b]; Mod[vx.vx, b]]; Seq = Function[{b, n}, Flatten[Position[Table[Ev[b, k], {k, 1, n}], 0]]]; Seq[3, 1000]

Crossrefs

Cf. A001969, A006287, A075311.

Sequence in context: A060275 A083984 A272022 * A076204 A267382 A135024

Adjacent sequences: A079492 A079493 A079494 * A079496 A079497 A079498

Keyword

base,easy,nonn

Author

Carlos Alves, Jan 20 2003

Extensions

Revised by Sean A. Irvine, Aug 17 2025

Status

approved