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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A262841

Adjacent sequences:  A177964 A177965 A177966 * A177968 A177969 A177970

KEYWORD

nonn

AUTHOR

Wouter Meeussen, May 16 2010

STATUS

approved

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Last modified December 11 03:29 EST 2018. Contains 318049 sequences. (Running on oeis4.)