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A064834 If n (in base 10) is d_1 d_2 ... d_k then a(n) = Sum_{i = 1..[k/2] } |d_i - d_{k-i+1}|.

%I A064834 #29 Apr 03 2020 17:55:09
%S A064834 0,0,0,0,0,0,0,0,0,0,1,0,1,2,3,4,5,6,7,8,2,1,0,1,2,3,4,5,6,7,3,2,1,0,
%T A064834 1,2,3,4,5,6,4,3,2,1,0,1,2,3,4,5,5,4,3,2,1,0,1,2,3,4,6,5,4,3,2,1,0,1,
%U A064834 2,3,7,6,5,4,3,2,1,0,1,2,8,7,6,5,4,3,2,1,0,1,9,8,7,6,5,4,3,2,1,0,1,0,1,2,3
%N A064834 If n (in base 10) is d_1 d_2 ... d_k then a(n) = Sum_{i = 1..[k/2] } |d_i - d_{k-i+1}|.
%C A064834 Might be called the Palindromic Deviation (or PD(n)) of n, since it measures how far n is from being a palindrome. - _W. W. Kokko_, Mar 13 2013
%C A064834 a(A002113(n)) = 0; a(A029742(n)) > 0; A136522(n) = A000007(a(n)). - _Reinhard Zumkeller_, Sep 18 2013
%H A064834 N. J. A. Sloane, <a href="/A064834/b064834.txt">Table of n, a(n) for n = 0..10000</a>
%H A064834 <a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>
%e A064834 a(456) = | 4 - 6 | = 2, a(4567) = | 4 - 7 | + | 5 - 6 | = 4.
%p A064834 f:=proc(n)
%p A064834 local t1,t2,i;
%p A064834 t1:=convert(n,base,10);
%p A064834 t2:=nops(t1);
%p A064834 add( abs(t1[i]-t1[t2+1-i]),i=1..floor(t2/2) );
%p A064834 end;
%p A064834 [seq(f(n),n=0..120)]; # _N. J. A. Sloane_, Mar 24 2013
%t A064834 f[n_] := (k = IntegerDigits[n]; l = Length[k]; Sum[ Abs[ k[[i]] - k[[l - i + 1]]], {i, 1, Floor[l/2] } ] ); Table[ f[n], {n, 0, 100} ]
%o A064834 (Haskell)
%o A064834 a064834 n = sum $ take (length nds `div` 2) $
%o A064834                   map abs $ zipWith (-) nds $ reverse nds
%o A064834    where nds = a031298_row n
%o A064834 -- _Reinhard Zumkeller_, Sep 18 2013
%o A064834 (Python)
%o A064834 from sympy import floor, ceiling
%o A064834 def A064834(n):
%o A064834     x, y = str(n), 0
%o A064834     lx2 = len(x)/2
%o A064834     for a,b in zip(x[:floor(lx2)],x[:ceiling(lx2)-1:-1]):
%o A064834         y += abs(int(a)-int(b))
%o A064834     return y
%o A064834 # _Chai Wah Wu_, Aug 09 2014
%Y A064834 Cf. A037904, A040163, A064844.
%Y A064834 Cf. A031298, A037888.
%K A064834 nonn,base,easy
%O A064834 0,14
%A A064834 _N. J. A. Sloane_, Oct 25 2001
%E A064834 More terms from _Vladeta Jovovic_, _Matthew Conroy_ and _Robert G. Wilson v_, Oct 26 2001