A240927 - OEIS

%I #17 Jun 24 2020 17:27:03

%S 11,22,33,44,55,66,77,88,99,1001,1010,1102,1111,1120,1203,1212,1221,

%T 1230,1304,1313,1322,1331,1340,1405,1414,1423,1432,1441,1450,1506,

%U 1515,1524,1533,1542,1551,1560,1607,1616,1625,1634,1643,1652,1661,1670,1708,1717

%N Positive integers with 2k digits (the first of which is not 0) where the sum of the first k digits equals the sum of the last k digits.

%C These integers are sometimes called balanced numbers.

%C There are 9, 615, 50412, 4379055, 392406145, ... 2k-digit balanced numbers with k >= 1.

%D Cambridge Colleges Sixth Term Examination Papers (STEP) 2007, Paper I, Section A (Pure Mathematics), Nr. 1.

%H Harvey P. Dale, <a href="/A240927/b240927.txt">Table of n, a(n) for n = 1..624</a> (* All terms through 9999 *)

%e 1423 is a 4-digit balanced number, because the sum of the first 2 digits equals the sum of the last 2 digits: 1 + 4 = 2 + 3.

%t sfslQ[n_]:=Module[{id=IntegerDigits[n],len},len=Length[id]/2;Total[Take[ id,len]]==Total[Take[id,-len]]]; Select[Table[Range[10^n,10^(n+1)-1],{n,1,3,2}]// Flatten,sfslQ] (* _Harvey P. Dale_, Jun 24 2020 *)

%Y Cf. A016061, A197083, A240928, A240929.

%K nonn,base

%O 1,1

%A _Martin Renner_, Aug 03 2014