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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}|. 11
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 COMMENTS 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 a(A002113(n)) = 0; a(A029742(n)) > 0; A136522(n) = A000007(a(n)). - Reinhard Zumkeller, Sep 18 2013 LINKS N. J. A. Sloane, Table of n, a(n) for n = 0..10000 Index entries for sequences related to palindromes EXAMPLE a(456) = | 4 - 6 | = 2, a(4567) = | 4 - 7 | + | 5 - 6 | = 4. MAPLE f:=proc(n) local t1, t2, i; t1:=convert(n, base, 10); t2:=nops(t1); add( abs(t1[i]-t1[t2+1-i]), i=1..floor(t2/2) ); end; [seq(f(n), n=0..120)]; # N. J. A. Sloane, Mar 24 2013 MATHEMATICA 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} ] PROG (Haskell) a064834 n = sum \$ take (length nds `div` 2) \$ map abs \$ zipWith (-) nds \$ reverse nds where nds = a031298_row n -- Reinhard Zumkeller, Sep 18 2013 (Python) from sympy import floor, ceiling def A064834(n): x, y = str(n), 0 lx2 = len(x)/2 for a, b in zip(x[:floor(lx2)], x[:ceiling(lx2)-1:-1]): y += abs(int(a)-int(b)) return y # Chai Wah Wu, Aug 09 2014 CROSSREFS Cf. A037904, A040163, A064844. Cf. A031298, A037888. Sequence in context: A037904 A070615 A040114 * A040163 A113608 A040115 Adjacent sequences: A064831 A064832 A064833 * A064835 A064836 A064837 KEYWORD nonn,base,easy AUTHOR N. J. A. Sloane, Oct 25 2001 EXTENSIONS More terms from Vladeta Jovovic, Matthew Conroy and Robert G. Wilson v, Oct 26 2001 STATUS approved

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Last modified April 22 04:43 EDT 2024. Contains 371887 sequences. (Running on oeis4.)