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a(0) = 1, a(1) = 3, a(2) = 13; for n >= 2, a(n+1) = 2*3^((a(n)-1)/4) - 1.
0

%I #12 Oct 16 2024 21:33:25

%S 1,3,13,53,3188645

%N a(0) = 1, a(1) = 3, a(2) = 13; for n >= 2, a(n+1) = 2*3^((a(n)-1)/4) - 1.

%C The next term is too large to include.

%C a(n) is the least positive integer that requires n steps to reach 1 under iteration of the sum of squares of digits function in base 3 (A006287).

%C a(n) is also the least positive integer that requires n steps to reach 1 under iteration of the map A375212.

%H N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.

%H G. Lapointe, <a href="https://arxiv.org/abs/1904.12032">On finding the smallest happy numbers of any heights</a>, arXiv:1904.12032 [math.NT], 2019.

%Y Cf. A006287, A007013, A375212.

%K nonn

%O 0,2

%A N. Bradley Fox, _Nathan Fox_, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024