A079342 Integers k that divide LS(k), where LS is the "Look and Say" function (A045918).

1, 2, 5, 10, 22, 32, 62, 91, 183, 188, 190, 196, 258, 276, 330, 671, 710, 1130, 1210, 1570, 2644, 2998, 3292, 4214, 17055, 20035, 53015, 70315, 101010, 108947, 199245, 233606, 309665, 323232, 356421, 483405, 626262, 919191, 1743599

Offset

1,2

Comments

Infinite since s^i is a term for all odd i and s = 10, 32, 62, 91, 183, 190, 196, 258, 276, 671, 710, 1210, 1570, ..., where ^ denotes repeated concatenation of digits. - Michael S. Branicky, Aug 28 2024

Links

Michael S. Branicky, Table of n, a(n) for n = 1..82 (all terms <= 10^10)

Example

E.g. LS(1)=11, LS(2)=12, LS(10)=1110, LS(188)=1128 etc. and in each case LS(n) is a multiple of n.
122918=0 mod 2998, so 2998 is in the sequence.
But 13 == 1 mod 3, so 3 is not in the sequence.

Maple

# Implementation by R. J. Mathar, May 08 2019:
A045918 := proc(n)
    local a, f, pd, dgs, i ;
    a := [] ;
    f := 0 ;
    pd := -1 ;
    dgs := convert(n, base, 10) ;
    for i from 1 to nops(dgs) do
        if op(-i, dgs) <> pd then
            if pd >= 0 then
                a := [op(a), f, pd] ;
            end if;
            pd := op(-i, dgs) ;
            f := 1 ;
        else
            f:= f+1 ;
        end if;
    end do:
    a := [op(a), f, pd] ;
    digcatL(%) ;
end proc:
isA079342 := proc(n)
    simplify( modp(A045918(n) , n) = 0 ) ;
end proc:
for n from 1 to 30000 do
    if isA079342(n) then
        print(n) ;
    end if;
end do:

Prog

(Python)
def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))
def ok(n): return LS(n)%n == 0
print([k for k in range(1, 10**4) if ok(k)]) # Michael S. Branicky, Aug 28 2024

Crossrefs

Cf. A056815, A005150, A079562.

Cf. A152957. - David Wasserman, Dec 15 2008

Sequence in context: A278441 A323939 A110744 * A034456 A272080 A002512

Adjacent sequences: A079339 A079340 A079341 * A079343 A079344 A079345

Keyword

base,nonn

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 13 2003

Status

approved