A193996 consists of numbers requiring exactly eight iterations to determine whether they are happy or not. While reviewing the entry, I noticed that the sequence has a simple structural description in terms of the dynamics of the sum-of-squares-of-digits map.
I proposed a clarification identifying A193996 as precisely the eight elements 4, 16, 37, 58, 89, 145, 42, and 20 of the nontrivial 8-cycle, together with the happy numbers of height 7. The revision was reviewed and published by OEIS editor Sean A. Irvine on September 9, 2026.
Structural characterization
The unhappy part of A193996 is exactly the nontrivial 8-cycle of the sum-of-squares-of-digits map. The remaining terms are happy numbers that require exactly seven further iterations to reach 1, so that determining their status requires eight iterations under the convention used by the sequence.
OEIS revision
I submitted this characterization as a new comment to A193996 on September 3, 2026. Sean A. Irvine reviewed the change, and OEIS confirmed on September 9, 2026 that my changes to A193996 had been published.