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A125886 a(1) = 1, a(n) = smallest positive number b not among a(1)..a(n-1) such that the last digit of b = the first digit of a(n-1).

%I A125886 #10 Aug 10 2014 11:14:27
%S A125886 1,11,21,12,31,13,41,14,51,15,61,16,71,17,81,18,91,19,101,111,121,131,
%T A125886 141,151,161,171,181,191,201,22,32,23,42,24,52,25,62,26,72,27,82,28,
%U A125886 92,29,102,211,112,221,122,231,132,241,142,251,152,261,162,271,172,281,182
%N A125886 a(1) = 1, a(n) = smallest positive number b not among a(1)..a(n-1) such that the last digit of b = the first digit of a(n-1).
%C A125886 A dyslexic person might have trouble distinguishing this sequence from A125887!
%C A125886 A010879(a(n+1)) = A000030(a(n)). - _Reinhard Zumkeller_, Aug 10 2014
%H A125886 Reinhard Zumkeller, <a href="/A125886/b125886.txt">Table of n, a(n) for n = 1..10000</a>
%H A125886 Hans Havermann, <a href="/A125886/a125886.png">Graph of first 10000 terms</a>
%t A125886 s={1}; fi=1; Do[Do[id=IntegerDigits[i]; la=id[[ -1]]; If[fi==la&&FreeQ[s,i],AppendTo[s,i]; fi=id[[1]]; Break[]],{i,11,10^5}],{999}]; s
%o A125886 (Haskell)
%o A125886 import Data.List (delete)
%o A125886 a125886 n = a125886_list !! (n-1)
%o A125886 a125886_list = 1 : f 1 [10..] where
%o A125886    f u vs = g vs where
%o A125886      g (w:ws) = if a010879 w == iu then w : f w (delete w vs) else g ws
%o A125886      iu = a000030 u
%o A125886 -- _Reinhard Zumkeller_, Aug 10 2014
%Y A125886 Cf. A125887.
%Y A125886 Cf. A000030, A010879.
%K A125886 base,nonn,look,hear
%O A125886 1,2
%A A125886 _Zak Seidov_, Dec 13 2006