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

1,3

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

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

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 *)

Prog

(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

Crossrefs

Cf. A004186, A033075.

Sequence in context: A255734 A357142 A033075 * A292439 A132577 A247167

Adjacent sequences: A215011 A215012 A215013 * A215015 A215016 A215017

Keyword

nonn,base,fini

Author

Tanya Khovanova and Charles R Greathouse IV, Jul 31 2012

Extensions

Name edited by Felix Fröhlich, Dec 26 2017

Status

approved