A248336 - OEIS

%I #9 Oct 13 2014 16:23:45

%S 0,10,12,1000,1022,100000,100222,10000000,10002222,1000000000,

%T 1000022222,100000000000,100000222222,10000000000000,10000002222222,

%U 1000000000000000,1000000022222222,100000000000000000,100000000222222222,10000000000000000000

%N Smallest number m such that the Levenshtein distance of m and its reversal equals n.

%C A248327(a(n)) = n and A248327(m) != n for m < a(n).

%F a(2*k) = 10^(2*k-1) + 2*(10^k-1)/9; a(2*k+1) = 10^(2*k+1).

%F Conjecture: a(n) = 111*a(n-2)-1110*a(n-4)+1000*a(n-6) for n>6. - _Colin Barker_, Oct 07 2014

%F 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

%o (Haskell)

%o import Data.List (elemIndex); import Data.Maybe (fromJust)

%o a248336 = fromJust . (`elemIndex` map a248327 [0..])

%o (PARI)

%o 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

%Y Cf. A004086, A248327.

%K nonn,base

%O 0,2

%A _Reinhard Zumkeller_, Oct 05 2014

%E Formula corrected by, and more terms from _Colin Barker_, Oct 07 2014