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

4,1

Comments

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

Links

Table of n, a(n) for n=4..44.

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

Prog

(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 <n);
vsearch(v, x) = for (i=1, #v, if (v[i] == x, return (i)); );
a(n) = {nmax = 0; for (i=0, n^n-1, d = digits(i, n); d = pad(d, n); circuit = [i]; pos = 0; if (isok(d, n), while (! pos, sd = say(d, n); if (! isok(sd, n), break); isd = fromdigits(sd, n); pos = vsearch(circuit, isd); if (! pos, circuit = concat(isd, circuit); d = sd, start = #circuit - pos; nmax = max(nmax, start); ); ); ); ); nmax; } \\ Michel Marcus, Feb 25 2017

Crossrefs

Cf. A046043, A108551.

Sequence in context: A316498 A200681 A161775 * A193967 A109823 A337124

Adjacent sequences: A282532 A282533 A282534 * A282536 A282537 A282538

Keyword

nonn,more

Author

Felix Fröhlich, Feb 17 2017

Extensions

Name edited by Michel Marcus, Feb 26 2017

Status

approved