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A249278 Lexicographically earliest permutation of the nonnegative integers such that the parity of the first digit of a(n+1) equals that of a(n)'s last digit.

%I A249278 #20 Dec 23 2024 14:53:44
%S A249278 0,2,4,6,8,20,21,1,3,5,7,9,10,22,23,11,12,24,25,13,14,26,27,15,16,28,
%T A249278 29,17,18,40,41,19,30,42,43,31,32,44,45,33,34,46,47,35,36,48,49,37,38,
%U A249278 60,61,39,50,62,63,51,52,64,65,53,54,66,67,55,56,68,69,57,58,80,81,59,70,82,83,71,72,84,85,73,74,86,87,75,76,88,89,77,78,200,201
%N A249278 Lexicographically earliest permutation of the nonnegative integers such that the parity of the first digit of a(n+1) equals that of a(n)'s last digit.
%C A249278 The inverse permutation is given in A249279. - _M. F. Hasler_, Oct 24 2014
%C A249278 A000030(a(n+1)) mod 2 = a(n) mod 2. - _Reinhard Zumkeller_, Oct 27 2014
%H A249278 Reinhard Zumkeller, <a href="/A249278/b249278.txt">Table of n, a(n) for n = 0..10000</a>
%H A249278 Éric Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-October/013865.html">Commas squeezed between two same parity digits</a>, SeqFan mailing list, Oct 24 2014
%H A249278 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A249278 (PARI) a(n,a=0,u=0)=for(n=1,n,for(k=0,9e9,!bittest(u,k)&&k\10^(#Str(k)-1)==Mod(a,2)&&!print1(a=k",")&&break);u+=1<<a);a \\ _M. F. Hasler_, Oct 24 2014
%o A249278 (Haskell)
%o A249278 a249278 n = a249278_list !! n
%o A249278 a249278_list = 0 : f 0 [1..] where
%o A249278    f u vs = g vs where
%o A249278      g (x:xs) = if (a000030 x) `mod` 2 == u `mod` 2
%o A249278                    then x : f x (delete x vs) else g xs
%o A249278 -- _Reinhard Zumkeller_, Oct 27 2014
%Y A249278 Cf. A000030, A249494 (variant starting with 1).
%K A249278 nonn,base
%O A249278 0,2
%A A249278 _Eric Angelini_, Oct 24 2014