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

1,1

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.

Links

Table of n, a(n) for n=1..50.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A318080 A066469 A318348 * A218626 A119149 A217658

Adjacent sequences: A197701 A197702 A197703 * A197705 A197706 A197707

Keyword

nonn,base

Author

Victor S. Miller, Oct 17 2011

Status

approved