A071887 Conjectured values of n whose trajectory under map x -> A002487(x)*A002487(x+1) does not go into a cycle.

37, 38, 41, 54, 57, 58, 68, 70

Offset

1,1

Comments

Why isn't 42 in this list? It does not enter a cycle in under 100 iterations which is as far as I could check. - Sean A. Irvine, Oct 05 2011

From William P. Orrick, May 02 2026: (Start)

The existing terms may be grouped according to their ultimate trajectory into the sets {37, 58}, {38, 57, 68, 70}, and {41, 54}.

If 2^k + m, with 0 <= m < 2^k, is in the sequence, then so is 2^(k+1) - 1 - m due to the symmetry of the irregular triangle A070871.

Known cycles include the seven cycles of length 1 implied by the known terms of A070872 and the cycles [36, 44, 60], [3498, 26496], and [11726, 53186, 49170]. Of positive integers less than or equal to 2^23, the number whose trajectory reaches a value exceeding 10^20 without entering any of these cycles is 8386858, or about 99.98%. Among these, the numbers less than 73 are the eight terms of this sequence and 42, 43, 52, 53, 65, 69, and 71. These last listed values all have the same ultimate trajectory. It remains unclear whether the terms with this trajectory were excluded from this sequence due to some unrecorded analysis. (End)

Links

Table of n, a(n) for n=1..8.

Crossrefs

Cf. A002487, A070871, A070872, A071884, A071885, A071886.

Sequence in context: A296871 A346383 A337453 * A168143 A111043 A041683

Adjacent sequences: A071884 A071885 A071886 * A071888 A071889 A071890

Keyword

nonn,more

Author

J. H. Conway, Jun 10 2002

Extensions

a(7)-a(8) from William P. Orrick, May 02 2026

Status

approved