A122002 a(0)=5; otherwise a(n) = (n mod 4) if n is odd, a(n) = h + 4, where h = (highest odd divisor of n) mod 4 if n is even.

5, 1, 5, 3, 5, 1, 7, 3, 5, 1, 5, 3, 7, 1, 7, 3, 5, 1, 5, 3, 5, 1, 7, 3, 7, 1, 5, 3, 7, 1, 7, 3, 5, 1, 5, 3, 5, 1, 7, 3, 5, 1, 5, 3, 7, 1, 7, 3, 7, 1, 5, 3, 5, 1, 7, 3, 7, 1, 5, 3, 7, 1, 7, 3, 5, 1, 5, 3, 5, 1, 7, 3, 5, 1, 5, 3, 7, 1, 7, 3, 5, 1, 5, 3, 5, 1, 7, 3, 7, 1, 5, 3, 7, 1, 7, 3, 7, 1, 5, 3, 5

Offset

0,1

Comments

a(n) in {1,3,5,7} for all n. a(4k+i) = i if i is odd.

There is a typo in Grytczuk's definition: he has "+ 5" instead of "+ 4".

Links

Table of n, a(n) for n=0..100.

A. Carpi, Multidimensional unrepetitive configurations, Theoret. Comput. Sci., 56 (1988), 233-241. a(n) = a_n of lemma 3.2 for the case p=2 and m=0 (which is corollary 3.3).

Jaroslaw Grytczuk, Thue type problems for graphs, points and numbers, Discrete Math., 308 (2008), 4419-4429. [See Problem 15.]

Jui-Yi Kao, Narad Rampersad, Jeffrey Shallit, Manuel Silva, Words Avoiding Repetitions in Arithmetic Progressions, Theoretical Computer Science, volume 391, issues 1-2, February 2008, pages 126-137.  And arXiv:math/0608607 [math.CO], 2006. (Extending to generalized paperfolding sequences.)

Index entries for sequences that are fixed points of mappings

Index entries for sequences related to squarefree words

Formula

Morphism 1 -> 5,3; 3 -> 7,3; 5 -> 5,1; 7 -> 7,1 starting from 5 [Carpi, h in remark after lemma 3.2]. - Kevin Ryde, Sep 09 2020

Prog

(PARI) a(n) = 2*if(n, bittest(n, valuation(n, 2)+1)) + if(n%2, 1, 5); \\ Kevin Ryde, Sep 09 2020

Crossrefs

Essentially the same: A112658 (map 1357 -> 0213), A125047 (map 1357 -> 2314).

Cf. A003324.

Sequence in context: A217774 A060186 A240995 * A322602 A228639 A073226

Adjacent sequences: A121999 A122000 A122001 * A122003 A122004 A122005

Keyword

nonn

Author

N. J. A. Sloane, Aug 05 2008

Extensions

Terms from a(26) on from John W. Layman, Aug 27 2008

Status

approved