A043096 Numbers in which every pair of adjacent digits are distinct.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 123, 124, 125, 126, 127, 128, 129

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• base

Comments

Superset of A010784. - R. J. Mathar, Oct 20 2008

Complement of A171901; A196368(a(n)) = 1. - Reinhard Zumkeller, Oct 28 2001

Examples

			11 is the first number not in the sequence, since it has a pair of identical adjacent digits.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010784, A171901, A196368.

Programs

Haskell

import Data.List (elemIndices)
a043096 n = a043096_list !! n
a043096_list = elemIndices 1 a196368_list
-- Reinhard Zumkeller, Oct 28 2001

Maple

isA034096 := proc(n)
    local dgs ;
    dgs := convert(n,base,10) ;
    for i from 2 to nops(dgs) do
        if op(i,dgs) = op(i-1,dgs) then
            return false;
        end if;
    end do:
    true ;
end proc:
for n from 0 to 150 do
    if isA034096(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jun 26 2023

Mathematica

t={}; Do[If[!MemberQ[Differences[IntegerDigits[n]], 0], AppendTo[t,n]], {n,0,69}]; t (* Jayanta Basu, May 04 2013 *)

PARI

is(n)=my(v=digits(n));for(i=2,#v,if(v[i]==v[i-1],return(0)));1 \\ Charles R Greathouse IV, Sep 17 2012

Python

def ok(n): s = str(n); return all(s[i] != s[i+1] for i in range(len(s)-1))
print(list(filter(ok, range(70)))) # Michael S. Branicky, Aug 22 2021

Extensions

Offset corrected by Reinhard Zumkeller, Oct 28 2011