A248336 Smallest number m such that the Levenshtein distance of m and its reversal equals n.
0, 10, 12, 1000, 1022, 100000, 100222, 10000000, 10002222, 1000000000, 1000022222, 100000000000, 100000222222, 10000000000000, 10000002222222, 1000000000000000, 1000000022222222, 100000000000000000, 100000000222222222, 10000000000000000000
Offset: 0
Programs
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Haskell
import Data.List (elemIndex); import Data.Maybe (fromJust) a248336 = fromJust . (`elemIndex` map a248327 [0..])
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PARI
s=[0, 10]; for(k=1, 12, s=concat(s, [10^(2*k-1)+2*(10^k-1)/9, 10^(2*k+1)])); s \\ Colin Barker, Oct 07 2014
Formula
a(2*k) = 10^(2*k-1) + 2*(10^k-1)/9; a(2*k+1) = 10^(2*k+1).
Conjecture: a(n) = 111*a(n-2)-1110*a(n-4)+1000*a(n-6) for n>6. - Colin Barker, Oct 07 2014
Empirical g.f.: -2*x*(50*x^5+50*x^4-155*x^3-55*x^2+6*x+5) / ((x-1)*(x+1)*(10*x-1)*(10*x+1)*(10*x^2-1)). - Colin Barker, Oct 07 2014
Extensions
Formula corrected by, and more terms from Colin Barker, Oct 07 2014
Comments