A107277 If n <= 1 then n else smallest number having in decimal representation exactly one common digit with its predecessor but none with its pre-predecessor.

0, 1, 12, 20, 30, 31, 41, 42, 52, 53, 63, 64, 74, 75, 85, 86, 96, 97, 107, 122, 233, 300, 401, 422, 523, 560, 611, 712, 730, 804, 811, 912, 930, 3444, 4111, 5001, 5222, 6233, 6400, 7011, 7222, 8233, 8400, 9011, 9222, 23333, 30000, 40111, 42222, 52333, 56000

Offset

0,3

Comments

Apparently the rules demand that a(n)>a(n-1) and that the "common" digit between a(n) and a(n-1) must appear only once in a(n). [Otherwise after 107 would follow 111.] - R. J. Mathar, May 05 2023

Links

R. J. Mathar, Table of n, a(n) for n = 0..73

Example

a(8)=52 and a(9)=53. a(10) cannot be any in the range 54..59 because these share the digit 5 with a(8) and a(9). a(10) cannot be in the range 60..62 because these do not have a common digit with 53. So a(10)=63. - R. J. Mathar, May 05 2023

Maple

freq := proc(L, n)
    local a;
    a := 0 ;
    for i from 1 to nops(L) do
        if op(i, L) = n then
            a := a+1 ;
        end if ;
    end do:
    a ;
end proc:
A107277 := proc(n)
    option remember ;
    local a, dgsa, pre, pre2, dgspre, dgspre2, cdig;
    if n <= 1 then
        n ;
    elif n =2 then
        12 ;
    else
        for a from procname(n-1)+1 do
            dgsa := convert(convert(a, base, 10), set) ;
            pre2 := procname(n-2) ;
            dgspre2 := convert(convert(pre2, base, 10), set) ;
            if dgspre2 intersect dgsa = {} then
                pre := procname(n-1) ;
                dgspre := convert(convert(pre, base, 10), set) ;
                cdig := dgsa intersect dgspre ;
                if nops(cdig) = 1 then
                    dgsa := convert(a, base, 10) ;
                    if freq(dgsa, op(cdig)) = 1 then
                        return a;
                    end if;
                end if;
            end if ;
        end do:
    end if;
end proc:
seq(A107277(n), n=0..60) ; # R. J. Mathar, May 05 2023

Crossrefs

Sequence in context: A364999 A366807 A210968 * A256883 A124672 A289980

Adjacent sequences: A107274 A107275 A107276 * A107278 A107279 A107280

Keyword

nonn,base

Author

Reinhard Zumkeller, May 19 2005

Status

approved