A145808 Non-palindromic balanced numbers: the first and the last half of digits have the same sum.

1010, 1102, 1120, 1203, 1212, 1230, 1304, 1313, 1322, 1340, 1405, 1414, 1423, 1432, 1450, 1506, 1515, 1524, 1533, 1542, 1560, 1607, 1616, 1625, 1634, 1643, 1652, 1670, 1708, 1717, 1726, 1735, 1744, 1753, 1762, 1780, 1809, 1818, 1827, 1836, 1845, 1854

Offset

1,1

Comments

Numbers such that the first half of digits have the same sum than the last half of digits are called balanced in the linked "Problem 217". (Note that here the meaning of "balanced" is neither that of A020492, nor that of A031443.)

Clearly all palindromes (A002113) have this property. Since the first non-palindromic example, 1010, comes only after A002113(109)=1001, we list here only non-palindromic balanced numbers.

Links

Zak Seidov, Table of n, a(n) for n=1..1000 [From _Zak Seidov_, Oct 20 2009]

Project Euler, Problem 217: Balanced Numbers.

Formula

A145808 = { m | A007953([m/10^A110654(A055642(m))]) = A007953(m mod 10^A004526(A055642(m))) } \ A002113

Mathematica

Reap[Do[id=IntegerDigits[n]; m=Floor[Length[id]/2]; If[Reverse[id]!=id&&Total[Take[id, m]]==Total[Take[id, -m]], Sow[n]], {n, 1010, 2000}]][[2, 1]] [From _Zak Seidov_, Oct 20 2009]
npbnQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Floor[Length[idn]/2]; idn!=Reverse[idn]&&Total[Take[idn, len]]==Total[Take[idn, -len]]]; Select[ Range[1000, 2000], npbnQ] (* _Harvey P. Dale_, Sep 25 2012 *)

Prog

(PARI) is_A145808(n) = is_balanced(n) & !is_A002113(n)
is_balanced(n) = { local( d, t=1+#Str(n)); (n\10^(t\2)-n%10^((t-1)\2)) % 9 && return; d=Vecsmall(Str(n)); sum(i=1, (t-1)\2, d[i]-d[t-i])==0 }

Crossrefs

Cf. A147808.

Sequence in context: A071998 A043640 A286138 * A252683 A157010 A076940

Adjacent sequences: A145805 A145806 A145807 * A145809 A145810 A145811

Keyword

base,easy,nice,nonn

Author

_M. F. Hasler_, Nov 17 2008

Status

approved