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

Author

Carlos Alves, Jan 20 2003

Keywords

• base
• easy
• nonn

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)

Examples

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

Crossrefs

Cf. A001969, A006287, A075311.

Programs

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]

Extensions

Revised by Sean A. Irvine, Aug 17 2025