A282535 a(n) is the maximum number of "describing"-steps for an n-chain before entering a loop.

3, 4, 7, 4, 7, 7, 7, 6, 7, 6, 7, 7, 7, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 4

Author

Felix Fröhlich, Feb 17 2017

Keywords

• nonn
• more

Comments

Conjecture: The size of terms of this sequence is unbounded (cf. Marichal, 2007, Corollary 5).

Links

• Jean-Luc Marichal, On perfect, amicable, and sociable chains, arXiv:0708.1491 [math.CO], 2007.

Crossrefs

Cf. A046043, A108551.

Programs

PARI

pad(d, n) = while(#d != n, d = concat([0], d)); d;
say(d, n) = vector(n, k, sum(j=1, #d, d[j] == (k-1)));
isok(v, n) = my(vs = vecsort(v,,8)); (#vs > 1) && (#vs Michel Marcus, Feb 25 2017

Extensions

Name edited by Michel Marcus, Feb 26 2017