A107043 Belgian-9 numbers.

9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 25, 27, 30, 32, 33, 36, 45, 51, 54, 57, 63, 67, 69, 72, 81, 83, 90, 93, 99, 100, 101, 102, 104, 105, 108, 109, 110, 111, 115, 117, 119, 120, 121, 122, 123, 124, 126, 129, 130, 135, 139, 140, 141, 142, 144, 146, 149, 153

Offset: 1

Author

Eric Angelini, Jun 07 2005

Keywords

• base
• easy
• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

See A106039 for definition and link.

Belgian-k numbers, k=0..9: A106039, A106439, A106518, A106596, A106631, A106792, A107014, A107018, A107032, A107043.

Cf. A257770.

Programs

Haskell

a107043 n = a107043_list !! (n-1)
a107043_list = filter belge9 [9..] where
   belge9 x = x == (head $ dropWhile (< x) $
                    scanl (+) 9 $ cycle (map (read . return) $ show x))
-- Reinhard Zumkeller, May 08 2015

Mathematica

belgianQ[n_, k_] := If[n < k, False, Block[{id = Join[{0}, IntegerDigits@ n]}, MemberQ[ Accumulate@ id, Mod[n - k, Plus @@ id]] ]]; Select[ Range@ 155, belgianQ[#, 9] &] (* Robert G. Wilson v, May 06 2011 *)

Extensions

Offset changed by Reinhard Zumkeller, May 08 2015