A060979 -id:A060979 - cp's OEIS frontend

A008593 Multiples of 11.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583

Offset: 0

N. J. A. Sloane

Numbers for which the sum of "digits" in base 100 is divisible by 11. For instance, 193517302 gives 1 + 93 + 51 + 73 + 02 = 220, and 2 + 20 = 22 = 2 * 11. - Daniel Forgues, Feb 22 2016

Numbers in which the sum of the digits in the even positions equals the sum of the digits in the odd positions. - Stefano Spezia, Jan 05 2025

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 323.
Tanya Khovanova, Recursive Sequences.
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008591, A008592, A008604, A059632; union of A135499 and A060979.

a008593 = (* 11)
a008593_list = [0, 11 ..]  -- Reinhard Zumkeller, Jul 05 2014

[11*n: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

g:=(1+10*z)/((1-z)): gser:=series(g, z=0, 88): seq((coeff(gser, z, n))*n, n=0..77); # Zerinvary Lajos, Feb 25 2009

Range[0, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

makelist(11*n,n,0,20); /* Martin Ettl, Dec 17 2012 */

a(n)=11*n \\ Charles R Greathouse IV, Nov 06 2014

a(n) = 11*n.
G.f.: 11*x/(1-x)^2. - David Wilding, Jun 21 2014
E.g.f.: 11*x*exp(x). - Stefano Spezia, Oct 08 2022
From Elmo R. Oliveira, Apr 10 2025: (Start)
a(n) = 2*a(n-1) - a(n-2).
a(n) = A008604(n)/2. (End)

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

Original entry on oeis.org

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

Paolo P. Lava and Giorgio Balzarotti, Feb 08 2008

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

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

Robert Israel, Table of n, a(n) for n = 1..10000 (first 119 terms from _Paolo P. Lava_ and _Giorgio Balzarotti_)

Cf. A067042, A214527.
Cf. A060979.
Cf. A225693.

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

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

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 *)

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A008593 Multiples of 11.

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