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

Author

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

Keywords

• base
• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A056815, A005150, A079562.

Cf. A152957. - David Wasserman, Dec 15 2008

Programs

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:

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