A108199 a(n) contains the digits of the remainder of a(n)/a(n-1). Sequence starts with 2.

2, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 25, 27, 29, 32, 35, 38, 42, 46, 51, 56, 62, 68, 75, 83, 92, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132

Offset

1,1

Comments

Clarifications: To reproduce the terms, only a(n) > a(n-1) are admitted. If the remainder is zero, that candidate a(n) is not admitted and the next larger a(n) is tested. (See the Maple implementation). Example: after 2, the candidates 3 to 9 are not admitted (remainder's digits are not subsets of candidate digits), but 10 (remainder 0) is also not admitted; finally 11 (remainder 11/2=1) follows 2. - R. J. Mathar, Feb 23 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 1..20000

Example

11 divided by 2 is 5 + remainder 1; "1" is in "11".
12 divided by 11 is 1 + remainder 1; "1" is in "12".

Maple

A108199 := proc(n)
    option remember ;
    local a, r, dgsa, dgsr ;
    if n =1 then
        2;
    else
        for a from procname(n-1)+1 do
            r := modp(a, procname(n-1)) ;
            if r > 0 then
                dgsa := convert(a, base, 10) ;
                dgsr := convert(r, base, 10) ;
                if verify(dgsr, dgsa, 'sublist') then
                    return a;
                end if;
            end if;
        end do:
    end if;
end proc:
seq(A108199(n), n=1..60) ; # R. J. Mathar, Jun 20 2021
# second Maple program:
d:= n-> {convert(n, base, 10)[]}:
a:= proc(n) option remember; local k; for k from 1+a(n-1) while
     (r-> r=0 or d(r) minus d(k)<>{})(irem(k, a(n-1))) do od; k
    end: a(1):=2:
seq(a(n), n=1..60);  # Alois P. Heinz, Mar 05 2024

Mathematica

l={2}; a[1]=2; k=2; Do[r=Mod[n, a[k-1]]; If[ContainsAny[IntegerDigits[r], IntegerDigits[n]], If[r>0, AppendTo[l, n]; a[k]=n; k++]], {n, 3, 127}]; l (* James C. McMahon, Feb 25 2024 *)

Crossrefs

Sequence in context: A068225 A367810 A043080 * A137904 A175414 A359220

Adjacent sequences: A108196 A108197 A108198 * A108200 A108201 A108202

Keyword

base,easy,nonn

Author

Eric Angelini, Jun 15 2005

Extensions

Offset set to 1 by R. J. Mathar, Jun 20 2021

Status

approved