A197704 Integers divisible by their generalized weight.

13, 18, 42, 60, 100, 115, 120, 145, 272, 279, 310, 319, 341, 372, 403, 434, 465, 480, 493, 496, 518, 540, 592, 595, 612, 665, 720, 748, 792, 805, 864, 884, 900, 918, 952, 1053, 1080, 1147, 1200, 1254, 1287, 1312, 1320, 1360, 1440, 1482, 1520, 1560, 1591, 1596

Offset: 1

Author

Victor S. Miller, Oct 17 2011

Keywords

• nonn
• base

Comments

The generalized weight of a binary number is obtained by assigning 1->3, 0->4, and summing up the weights of the digits (no leading zeros), for example 13 is in the sequence because it's 1101 in binary.

Crossrefs

Cf. A177869 (same sort of sequence in which each digit gets weight 1).

Programs

Haskell

base_weight b g n | n == 0 = 0 | otherwise = (base_weight b g (n `div` b)) + (g $ n `mod` b)
interesting b g = filter f [1..] where f n = n `mod` (base_weight b g n) == 0
bin_interesting g = interesting 2 g
weights l n | (n >=0) && ((length l) > fromInteger n) = l !! fromInteger n | otherwise = 0
original = weights [4,3]
let a = bin_interesting original

Mathematica

Select[Range[2000], IntegerQ[#/Plus@@(IntegerDigits[#, 2]/.{1 -> 3, 0 -> 4})] &] (* Alonso del Arte, Oct 17 2011 *)

PARI

is(n)=my(v=binary(n));n%(#v<<2-sum(i=1,#v,v[i]))==0 \\ Charles R Greathouse IV, Oct 19 2011