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A145808
Non-palindromic balanced numbers: the first and the last half of digits have the same sum.
3
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]
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
KEYWORD
base,easy,nice,nonn
AUTHOR
M. F. Hasler, Nov 17 2008
STATUS
approved