A032981 Positive numbers with the property that all pairs of consecutive base-10 digits differ by 0 or 1.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 101, 110, 111, 112, 121, 122, 123, 210, 211, 212, 221, 222, 223, 232, 233, 234, 321, 322, 323, 332, 333, 334, 343, 344, 345

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

a(n) = A178403(n+1) for n < 38. - Reinhard Zumkeller, May 27 2010

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A068148 (primes).

Programs

Haskell

a032981 n = a032981_list !! (n-1)
a032981_list = map read $ filter f $ map show [1..] :: [Int] where
   f ps = all (`elem` neighbours) $ zipWith ((. return) . (:)) ps (tail ps)
   neighbours = "09" : "90" : zipWith ((. return) . (:))
      (digs ++ tail digs ++ init digs) (digs ++ init digs ++ tail digs)
   digs = "0123456789"
-- Reinhard Zumkeller, Feb 14 2015

Mathematica

okQ[n_]:=Max[Abs[Last[#]-First[#]]&/@Partition[IntegerDigits[n],2,1]]<2
Select[Range[350],okQ]  (* Harvey P. Dale, Feb 14 2011 *)