A125047 Infinite word generated by mapping 1->12, 2->13, 3->43, 4->42 starting at 1.

1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 4, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 1, 2, 1, 3, 4, 2, 4, 3, 1, 2, 1, 3, 1, 2, 4, 3, 4, 2, 1, 3, 4, 2, 4, 3, 4, 2, 1, 3, 1, 2, 4, 3, 1

Offset: 1

Author

Michael Somos, Nov 17 2006

Keywords

• nonn

Comments

Infinite word over 4-letter alphabet that contains no squares in arithmetic progressions of odd difference. - Ralf Stephan, May 09 2007

Examples

			1 -> 12 -> 1213 -> 12131242 -> 1213124312134243 -> ...
		

Links

• 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.
• Index entries for sequences that are fixed points of mappings

Crossrefs

Essentially the same: A112658 (map 1234 -> 1023), A122002 (map 1234 -> 5137).

Cf. A038190.

Programs

Mathematica

SubstitutionSystem[{1 -> {1, 2}, 2 -> {1, 3}, 3 -> {4, 3}, 4 -> {4, 2}}, {1}, 7] // Last (* Jean-François Alcover, Dec 17 2018 *)

PARI

{a(n)=local(A); if(n<1, 0, A=[1]; while(length(A)
				

PARI

my(table=[1,2;4,3]); a(n) = n--; table[if(n,bittest(n,1+valuation(n,2)))+1, n%2+1]; \\ Kevin Ryde, Sep 05 2020

Formula

Recurrence: a(1)=1, a(4n)=3, a(4n+2)=2, a(8n+3)=1, a(8n+7)=4, a(4n+1)=a(2n+1). - Ralf Stephan, May 09 2007