A177967 a(n) is the least integer such that the iterated modulus chain m_1=mod(a(n),m),m_2=mod(a(n),m_1),m_3=mod(a(n),m_2),..., m_n= (0 or 1) reaches a length n. The companion value m, associated to a(n), is given in A177968.

2, 3, 5, 8, 11, 19, 34, 46, 53, 95, 103, 179, 251, 299, 503, 743, 1006, 1319, 1439, 2878, 3359, 3959, 6619, 5387, 10774, 5879, 11758, 17747, 24373, 40679, 26879, 35279, 61739, 23399, 46798

Offset

1,1

Comments

Apart from 8, seems to consist of primes or a product of two primes.

Links

Table of n, a(n) for n=1..35.

Example

3 mod 2 =1
5 mod 3 =2 ;5 mod 2 =1
8 mod 5 =3 ;8 mod 3 =2; 8 mod 2 =0
11 mod 7 =4; 11 mod 4 =3; 11 mod 3 =2; 11 mod 2= 1
or, as a triangular table:
1
2;1
3;2;1
5;3;2;1
8;5;3;2;0
11;7;4;3;2;1
19;12;7;5;4;3;1
34;25;9;7;6;4;2;0

Mathematica

modlen[n_, m_]:= Length[NestWhileList[Mod[n, #1]&, m, #1>1&]];
Table[Max[modlen[n, #1]& /@ Range[Floor[n/2]]], {n, 70000}]; Flatten[Position[%, #, 1, 1]&/@ Range[64]]; Function[n, modlen[n, #1]& /@ Range[Floor[n/2]]]/@ %; Flatten[First /@ (Position[ #, Max[ # ]]&/@ %)]; Drop[Transpose[{%%%, %}], 2]

Crossrefs

Cf. A177968

Sequence in context: A254308 A119014 A006258 * A265741 A254351 A346116

Adjacent sequences: A177964 A177965 A177966 * A177968 A177969 A177970

Keyword

nonn

Author

Wouter Meeussen, May 16 2010

Status

approved