A378624 Numbers whose binary representation interpreted as being base-3 is divisible by 5.

0, 5, 10, 15, 19, 20, 30, 38, 40, 45, 49, 59, 60, 65, 75, 76, 80, 85, 90, 95, 98, 103, 105, 118, 120, 125, 130, 135, 137, 150, 152, 157, 160, 165, 170, 175, 179, 180, 190, 195, 196, 206, 210, 215, 217, 225, 235, 236, 240, 245, 250, 255, 259, 260, 270, 274, 279, 281, 289, 299

Offset: 1

Author

Kyle David Krueger, Dec 02 2024

Keywords

• nonn
• base

Comments

This sequence is infinite. Given any arbitrarily large number, the last 4 binary bits can be set to 0, and, if this number does not already meet the criteria, one of the last 4 bits can be increased to 1 such that it does.

Examples

			19 is a term: 19 = 10011_2 -> 10011_3 = 85 = 17 * 5.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001969, A079498.

Programs

Mathematica

Select[Range[0, 300], Divisible[FromDigits[IntegerDigits[#, 2], 3], 5] &] (* Paolo Xausa, Dec 22 2024 *)

PARI

is(n) = fromdigits(binary(n),3)%5 == 0 \\ David A. Corneth, Dec 02 2024