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%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
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