%I #6 Mar 30 2014 12:56:37

%S 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,22,23,24,25,26,27,28,29,

%T 33,34,35,36,37,38,39,44,45,46,47,48,49,55,56,57,58,59,66,67,68,69,77,

%U 78,79,88,89,99,111,112,113,114,115,116,117,118,119,122,123,124,125,126,127,128,129,133

%N "True already", base 10, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 1.

%C Conjecture: this sequence in various bases never includes a term divisible by the base.

%D Inspired by discussion of "True so far" from _Eric Angelini_ (A102357).

%e The first 9 values of the sequence written in decimal include no '0's and 1 '1', so the next value cannot be 10 (the count of '0's is not 1) but can be 11.

%p A102827aux := proc(n,dig)

%p local c,d ;

%p c := 0 ;

%p for d in convert(n,base,10) do

%p if d = dig then

%p c := c+1 ;

%p end if;

%p end do:

%p c ;

%p end proc:

%p A102827 := proc(n)

%p option remember;

%p local a,a10,ad,cum;

%p if n < 8 then

%p return n+1 ;

%p end if;

%p for a from 1 do

%p a10 := floor(a/10) ;

%p ad := a mod 10 ;

%p cum := add( A102827aux(procname(i),ad),i=0..n-1) ;

%p if cum = a10 then

%p return a;

%p end if;

%p end do:

%p end proc: # _R. J. Mathar_, Mar 30 2014

%Y Cf. A102823-A102830, A102357.

%K nonn,easy,base

%O 0,2

%A _Hugo van der Sanden_, Feb 26 2005