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

11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 220, 231, 242, 253, 264, 275, 286, 297, 330, 341, 352, 363, 374, 385, 396, 440, 451, 462, 473, 484, 495, 550, 561, 572, 583, 594, 660, 671, 682, 693, 770, 781, 792, 880, 891, 990

Offset

1,1

Comments

Conjecture: this is a subsequence of A008593 (verified for the first 50 thousand terms). - R. J. Mathar, Feb 10 2008

Subsequence of A008593. - Zak Seidov Feb 11 2008

If k is present, so is 10*k. - Robert G. Wilson v, Jul 13 2014

As Seidov said, a subsequence of multiples of 11. That follows trivially from the divisibility rule for 11. - Jens Kruse Andersen, Jul 13 2014

A225693(a(n)) = 0. - Reinhard Zumkeller, Aug 08 2014

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 119 terms from Paolo P. Lava and Giorgio Balzarotti)

Example

594, 1023, and 1397 are terms:
   594 -> 4 + 5 = 9;
  1023 -> 3 + 0 = 2 + 1;
  1397 -> 7 + 3 = 9 + 1.

Maple

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);
# Alternative:
filter:= proc(n)
local L, d;
L:= convert(n, base, 10);
d:= nops(L);
add(L[2*i], i=1..floor(d/2)) = add(L[2*i-1], i=1..floor((d+1)/2))
end proc:
select(filter, [ 11*j $ j= 1 .. 10^4 ]); # Robert Israel, May 28 2014

Mathematica

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 *)

Prog

(Haskell)
a135499 n = a135499_list !! (n-1)
a135499_list = filter ((== 0) . a225693) [1..]
-- Reinhard Zumkeller, Aug 08 2014, Jul 05 2014

Crossrefs

Cf. A067042, A214527.

Cf. A060979.

Cf. A225693.

Sequence in context: A048841 A059632 A008593 * A080195 A004920 A136613

Adjacent sequences: A135496 A135497 A135498 * A135500 A135501 A135502

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, Feb 08 2008

Status

approved