A079342 - OEIS

%I #24 Aug 29 2024 01:19:11

%S 1,2,5,10,22,32,62,91,183,188,190,196,258,276,330,671,710,1130,1210,

%T 1570,2644,2998,3292,4214,17055,20035,53015,70315,101010,108947,

%U 199245,233606,309665,323232,356421,483405,626262,919191,1743599

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

%C 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

%H Michael S. Branicky, <a href="/A079342/b079342.txt">Table of n, a(n) for n = 1..82</a> (all terms <= 10^10)

%e 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.

%e 122918=0 mod 2998, so 2998 is in the sequence.

%e But 13 == 1 mod 3, so 3 is not in the sequence.

%p # Implementation by _R. J. Mathar_, May 08 2019:

%p A045918 := proc(n)

%p     local a,f,pd,dgs,i ;

%p     a := [] ;

%p     f := 0 ;

%p     pd := -1 ;

%p     dgs := convert(n,base,10) ;

%p     for i from 1 to nops(dgs) do

%p         if op(-i,dgs) <> pd then

%p             if pd >= 0 then

%p                 a := [op(a),f,pd] ;

%p             end if;

%p             pd := op(-i,dgs) ;

%p             f := 1 ;

%p         else

%p             f:= f+1 ;

%p         end if;

%p     end do:

%p     a := [op(a),f,pd] ;

%p     digcatL(%) ;

%p end proc:

%p isA079342 := proc(n)

%p     simplify( modp(A045918(n) ,n) = 0 ) ;

%p end proc:

%p for n from 1 to 30000 do

%p     if isA079342(n) then

%p         print(n) ;

%p     end if;

%p end do:

%o (Python)

%o def LS(n): return int(''.join(str(len(list(g)))+k for k, g in groupby(str(n))))

%o def ok(n): return LS(n)%n == 0

%o print([k for k in range(1, 10**4) if ok(k)]) # _Michael S. Branicky_, Aug 28 2024

%Y Cf. A056815, A005150, A079562.

%Y Cf. A152957. - _David Wasserman_, Dec 15 2008

%K base,nonn

%O 1,2

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