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A135499 Numbers for which Sum_digits(odd positions) = Sum_digits(even positions).

%I A135499 #32 May 09 2021 11:19:44
%S A135499 11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,198,220,
%T A135499 231,242,253,264,275,286,297,330,341,352,363,374,385,396,440,451,462,
%U A135499 473,484,495,550,561,572,583,594,660,671,682,693,770,781,792,880,891,990
%N A135499 Numbers for which Sum_digits(odd positions) = Sum_digits(even positions).
%C A135499 Conjecture: this is a subsequence of A008593 (verified for the first 50 thousand terms). - _R. J. Mathar_, Feb 10 2008
%C A135499 Subsequence of A008593. - _Zak Seidov_ Feb 11 2008
%C A135499 If k is present, so is 10*k. - _Robert G. Wilson v_, Jul 13 2014
%C A135499 As Seidov said, a subsequence of multiples of 11. That follows trivially from the divisibility rule for 11. - _Jens Kruse Andersen_, Jul 13 2014
%C A135499 A225693(a(n)) = 0. - _Reinhard Zumkeller_, Aug 08 2014
%H A135499 Robert Israel, <a href="/A135499/b135499.txt">Table of n, a(n) for n = 1..10000</a> (first 119 terms from _Paolo P. Lava_ and _Giorgio Balzarotti_)
%e A135499 594, 1023, and 1397 are terms:
%e A135499    594 -> 4 + 5 = 9;
%e A135499   1023 -> 3 + 0 = 2 + 1;
%e A135499   1397 -> 7 + 3 = 9 + 1.
%p A135499 P:=proc(n) local i,k,w,x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=0; k:=i; while k>0 do x:=x+(k-(trunc(k/10)*10)); k:=trunc(k/100); od; if w=2*x then print(i); fi; od; end: P(3000);
%p A135499 # Alternative:
%p A135499 filter:= proc(n)
%p A135499 local L,d;
%p A135499 L:= convert(n,base,10);
%p A135499 d:= nops(L);
%p A135499 add(L[2*i],i=1..floor(d/2)) = add(L[2*i-1],i=1..floor((d+1)/2))
%p A135499 end proc:
%p A135499 select(filter,[ 11*j $ j= 1 .. 10^4 ]); # _Robert Israel_, May 28 2014
%t A135499 dQ[n_]:=Module[{p=Transpose[Partition[IntegerDigits[n],2,2,1,0]]},Total[First[p]]== Total[Last[p]]]; Select[Range[1000],dQ] (* _Harvey P. Dale_, May 26 2011 *)
%o A135499 (Haskell)
%o A135499 a135499 n = a135499_list !! (n-1)
%o A135499 a135499_list = filter ((== 0) . a225693) [1..]
%o A135499 -- _Reinhard Zumkeller_, Aug 08 2014, Jul 05 2014
%Y A135499 Cf. A067042, A214527.
%Y A135499 Cf. A060979.
%Y A135499 Cf. A225693.
%K A135499 easy,nonn,base
%O A135499 1,1
%A A135499 _Paolo P. Lava_ and _Giorgio Balzarotti_, Feb 08 2008