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

1,1

Comments

These integers are sometimes called balanced numbers.

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

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 *)

Example

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.

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 *)

Crossrefs

Cf. A016061, A197083, A240928, A240929.

Sequence in context: A241899 A226468 A283871 * A272655 A333440 A056524

Adjacent sequences: A240924 A240925 A240926 * A240928 A240929 A240930

Keyword

nonn,base

Author

Martin Renner, Aug 03 2014

Status

approved