A215014 Numbers where any two consecutive decimal digits differ by 1 after arranging the digits in decreasing order.

0, 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, 102, 120, 123, 132, 201, 210, 213, 231, 234, 243, 312, 321, 324, 342, 345, 354, 423, 432, 435, 453, 456, 465, 534, 543, 546, 564, 567, 576, 645, 654, 657, 675, 678, 687, 756, 765, 768, 786, 789, 798, 867

Offset: 1

Author

Tanya Khovanova and Charles R Greathouse IV, Jul 31 2012

Keywords

• nonn
• base
• fini

Comments

a(4091131) = 9876543210 is the last term.

Numbers n such that A004186(n) is a term of A033075. - Felix Fröhlich, Dec 26 2017

Also 0 together with positive integers having k distinct digits and the difference between the largest and the smallest digit equal to k-1. - David A. Corneth, Dec 26 2017

Links

• Ely Golden, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004186, A033075.

Programs

Mathematica

lst = {}; Do[If[Times @@ Differences@Sort@IntegerDigits[n] == 1, AppendTo[lst, n]], {n, 0, 675}]; lst (* Arkadiusz Wesolowski, Aug 01 2012 *)
Join[Range[0,9],Select[Range[1000],Union[Differences[Sort[ IntegerDigits[ #]]]] == {1}&]] (* Harvey P. Dale, Jan 14 2015 *)

PARI

is(n)=my(v=vecsort(eval(Vec(Str(n)))));for(i=2,#v,if(v[i]!=1+v[i-1],return(0)));1

PARI

is(n) = if(!n, return(1)); my(d = digits(n), v = vecsort(d,,8)); #d == #v && v[#v] - v[1] == #v - 1

Python

# Ely Golden, Dec 26 2017
def consecutive(li):
  for i in range(len(li)-1):
    if(li[i+1]!=1+li[i]): return False
  return True
def sorted_digits(n):
  lst=[]
  while(n>0):
    lst+=[n%10] ; n//=10
  lst.sort() ; return lst
j=0
for i in range(1,10001):
  while(not consecutive(sorted_digits(j))): j+=1
  print(str(i)+" "+str(j)) ; j+=1

Python

# alternate for generating full sequence in seconds
from itertools import permutations as perms
frags = ["0123456789"[i:j] for i in range(10) for j in range(i+1, 11)]
afull = sorted(set(int("".join(s)) for f in frags for s in perms(f)))
print(afull[:70]) # Michael S. Branicky, Aug 04 2022

Formula

If zero is excluded, the number of terms with k digits, 1 <= k <= 10, is (11-k)*k! - (k-1)!. - Franklin T. Adams-Watters, Aug 01 2012

Extensions

Name edited by Felix Fröhlich, Dec 26 2017