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.

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, 29, 17, 18, 40, 41, 19, 30, 42, 43, 31, 32, 44, 45, 33, 34, 46, 47, 35, 36, 48, 49, 37, 38, 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

Offset: 0

Author

Eric Angelini, Oct 24 2014

Keywords

• nonn
• base

Comments

The inverse permutation is given in A249279. - M. F. Hasler, Oct 24 2014

A000030(a(n+1)) mod 2 = a(n) mod 2. - Reinhard Zumkeller, Oct 27 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Éric Angelini, Commas squeezed between two same parity digits, SeqFan mailing list, Oct 24 2014
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A000030, A249494 (variant starting with 1).

Programs

Haskell

a249278 n = a249278_list !! n
a249278_list = 0 : f 0 [1..] where
   f u vs = g vs where
     g (x:xs) = if (a000030 x) `mod` 2 == u `mod` 2
                   then x : f x (delete x vs) else g xs
-- Reinhard Zumkeller, Oct 27 2014

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<M. F. Hasler, Oct 24 2014