%I #15 Feb 22 2013 21:38:31

%S 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,

%T 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,

%U 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

%N Characteristic function of mountain numbers.

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

%C a(n) = 0 for n > 12345678987654321;

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

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

%H R. Zumkeller, <a href="/A178333/b178333.txt">Table of n, a(n) for n = 0..20000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

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

%F 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)

%F 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.

%t 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 *)

%o (Haskell)

%o a178333 n = fromEnum $

%o n `mod` 10 == 1 && a000030 n == 1 && a196368 n == 1 && and down where

%o down = dropWhile (== False) $ zipWith (<) (tail $ show n) (show n)

%o a178333_list = map a178333 [0..]

%o -- _Reinhard Zumkeller_, Oct 28 2001

%Y Cf. A000030, A196368.

%K nonn,base

%O 0,1

%A _Reinhard Zumkeller_, May 25 2010