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

Author

M. F. Hasler, Nov 17 2008

Keywords

• base
• easy
• nice
• nonn

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.

Crossrefs

Cf. A147808.

Programs

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]] (* 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 *)

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 }

Formula

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