A033075 Positive numbers all of whose pairs of consecutive decimal digits differ by 1.
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 101, 121, 123, 210, 212, 232, 234, 321, 323, 343, 345, 432, 434, 454, 456, 543, 545, 565, 567, 654, 656, 676, 678, 765, 767, 787, 789, 876
Offset: 1
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- J. M. De Koninck and N. Doyon, Esthetic numbers, Annales des Sciences mathématiques du Québec, 33 (2009), 155-164.
Programs
-
Haskell
-- import Data.Set (fromList, deleteFindMin, insert) a033075 n = a033075_list !! (n-1) a033075_list = f (fromList [1..9]) where f s | d == 0 = m : f (insert (10*m+1) s') | d == 9 = m : f (insert (10*m+8) s') | otherwise = m : f (insert (10*m+d-1) (insert (10*m+d+1) s')) where (m,s') = deleteFindMin s d = mod m 10 -- Reinhard Zumkeller, Feb 21 2012 -
Mathematica
Join[Range[9],Select[Range[2000],Union[Abs[Differences[IntegerDigits[#]]]]=={1}&]] (* Harvey P. Dale, Dec 28 2011 *) -
PARI
diff(v)=vector(#v-1,i,v[i+1]-v[i]) is(n)=if(n>9, Set(abs(diff(digits(n))))==[1], n>0) \\ Charles R Greathouse IV, Mar 11 2014
-
Python
def ok(n): s = str(n) return all(abs(int(s[i]) - int(s[i+1])) == 1 for i in range(len(s)-1)) print(list(filter(ok, range(1, 877)))) # Michael S. Branicky, Aug 22 2021 -
Python
# faster version for initial segment of sequence def gen(d, s=None): # generate remaining d digits, from start digit s if d == 0: yield tuple() return if s == None: yield from [(i, ) + g for i in range(1, 10) for g in gen(d-1, s=i)] else: if s > 0: yield from [(s-1, ) + g for g in gen(d-1, s=s-1)] if s < 9: yield from [(s+1, ) + g for g in gen(d-1, s=s+1)] def agentod(digits): for d in range(1, digits+1): yield from [int("".join(map(str, g))) for g in gen(d, s=None)] print(list(agentod(11))) # Michael S. Branicky, Aug 22 2021
Formula
a(n) >> n^3.53267..., where the exponent is log 10/log k and k is the largest root of x^5 - x^4 - 4x^3 + 3x^2 + 3x - 1. - Charles R Greathouse IV, Mar 11 2014
Comments