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

0,1

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).

Links

R. Zumkeller, Table of n, a(n) for n = 0..20000

Index entries for characteristic functions

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

Cf. A000030, A196368.

Sequence in context: A173950 A157928 A159075 * A063524 A326168 A033683

Adjacent sequences: A178330 A178331 A178332 * A178334 A178335 A178336

Keyword

nonn,base

Author

Reinhard Zumkeller, May 25 2010

Status

approved