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A178333
Characteristic function of mountain numbers.
5
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
0,1
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).
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.
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 *)
PROG
(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
CROSSREFS
Sequence in context: A173950 A157928 A159075 * A063524 A326168 A033683
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, May 25 2010
STATUS
approved