A249278 - OEIS

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

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OFFSET

0,2

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

PROG

(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

(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

CROSSREFS

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

Sequence in context: A323333 A076402 A053198 * A273892 A352546 A179082

Adjacent sequences: A249275 A249276 A249277 * A249279 A249280 A249281

KEYWORD

nonn,base

AUTHOR

Eric Angelini, Oct 24 2014

STATUS

approved