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
KEYWORD
easy,nonn,base
AUTHOR
Paolo P. Lava and Giorgio Balzarotti, Feb 08 2008
STATUS
approved