A240927 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.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1001, 1010, 1102, 1111, 1120, 1203, 1212, 1221, 1230, 1304, 1313, 1322, 1331, 1340, 1405, 1414, 1423, 1432, 1441, 1450, 1506, 1515, 1524, 1533, 1542, 1551, 1560, 1607, 1616, 1625, 1634, 1643, 1652, 1661, 1670, 1708, 1717

Offset: 1

Author

Martin Renner, Aug 03 2014

Keywords

• nonn
• base

Comments

These integers are sometimes called balanced numbers.

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

Examples

			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.
		

References

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..624 (All terms through 9999)

Crossrefs

Cf. A016061, A197083, A240928, A240929.

Programs

Mathematica

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 *)