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

1,3

Comments

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

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A010784, A171901, A196368.

Sequence in context: A160542 A241158 A241157 * A355301 A010784 A052081

Adjacent sequences: A043093 A043094 A043095 * A043097 A043098 A043099

Keyword

nonn,base

Author

Clark Kimberling

Extensions

Offset corrected by Reinhard Zumkeller, Oct 28 2011

Status

approved