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A135499 Numbers for which Sum_digits(odd positions)=Sum_digits(even positions). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

Subset 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 subset 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 -> 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

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)