A178333 Characteristic function of mountain numbers.

0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Reinhard Zumkeller, May 25 2010

Keywords

• nonn
• base

Comments

a(A134941(n)) = 1; a(A134951(n)) = 1;

a(n) = 0 for n > 12345678987654321;

a(A011540(n))=0; a(A052383(n))=0; a(A171901(n))=0;

A178334(n) = SUM(a(k): 0<=k<=n).

Links

• R. Zumkeller, Table of n, a(n) for n = 0..20000
• Index entries for characteristic functions

Crossrefs

Cf. A000030, A196368.

Programs

Haskell

a178333 n = fromEnum $
   n `mod` 10 == 1 && a000030 n == 1 && a196368 n == 1 && and down where
      down = dropWhile (== False) $ zipWith (<) (tail $ show n) (show n)
a178333_list = map a178333 [0..]
-- Reinhard Zumkeller, Oct 28 2001

Mathematica

a[n_] := Boole[ MatchQ[ IntegerDigits[n], {1, a___, b_, c___, 1} /; OrderedQ[{1, a, b}, Less] && OrderedQ[ {b, c, 1}, Greater]]]; a[1]=1; Table[a[n], {n, 0, 200}] (* Jean-François Alcover, Jun 13 2012 *)

Formula

a(n) = if n mod 10 = 1 then if n = 1 then 1 else g(n div 10, 1) else 0

with g(x, y) = if x mod 10 > y then g(x div 10, x mod 10) else if x mod 10 = y then 0 else h(x div 10, x mod 10)

and h(x, y) = if y = 1 then 0^x else if x mod 10 < y then h(x div 10, x mod 10) else 0.