A197704 - OEIS

%I #25 Mar 01 2024 02:04:52

%S 13,18,42,60,100,115,120,145,272,279,310,319,341,372,403,434,465,480,

%T 493,496,518,540,592,595,612,665,720,748,792,805,864,884,900,918,952,

%U 1053,1080,1147,1200,1254,1287,1312,1320,1360,1440,1482,1520,1560,1591,1596

%N Integers divisible by their generalized weight.

%C 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.

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

%o (Haskell)

%o base_weight b g n | n == 0 = 0 | otherwise = (base_weight b g (n `div` b)) + (g $ n `mod` b)

%o interesting b g = filter f [1..] where f n = n `mod` (base_weight b g n) == 0

%o bin_interesting g = interesting 2 g

%o weights l n | (n >=0) && ((length l) > fromInteger n) = l !! fromInteger n | otherwise = 0

%o original = weights [4,3]

%o let a = bin_interesting original

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

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

%K nonn,base

%O 1,1

%A _Victor S. Miller_, Oct 17 2011