A122002 - OEIS

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

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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

MATHEMATICA

a[0]=5; a[n_]:=If[OddQ[n], Mod[n, 4], 4+Mod[Select[Divisors[n], OddQ][[-1]], 4]]; Table[a[n], {n, 0, 100}] (* James C. McMahon, Oct 25 2024 *)

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