cp's OEIS Frontend

A377087 Number of cycles under iteration of the map sending a positive integer to the product of its leading base-n digit and the sum of the squares of its base-n digits.

%I A377087 #7 Oct 16 2024 20:56:06
%S A377087 0,1,0,1,2,1,2,0,3,2,5,2,4,1,3,3,3,2,3,4,1,5,3,7,2,3,3,3,4,4,5,3,6,12,
%T A377087 2,1,3,2,6,10,4,8,6,3,4,2,3,1,3,4,9,3,2,2,5,7,4,8,7,5,6,6,6,1,8,7,4,6,
%U A377087 6,2,5,7,5,5,4,5,3,4,3,5,2,4,7,8,3,7,7
%N A377087 Number of cycles under iteration of the map sending a positive integer to the product of its leading base-n digit and the sum of the squares of its base-n digits.
%C A377087 If b>=2 and a>=b^3 then E(a,2,b)<a. For each positive integer a, there is an positive integer m such that E^m(a,2,b)<b^3. (Fox et al., 2024, Lemma 4).
%H A377087 Nathan Fox, <a href="/A377087/b377087.txt">Table of n, a(n) for n = 2..100</a>
%H A377087 N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.
%e A377087 In the decimal system all integers go to (1), (298), (46, 208, 136), (26, 80, 512, 150), or (33, 54, 205, 58, 445, 228, 144) under iteration of the map A376270, hence there are two fixed points and three cycles. Therefore a(10) = 3.
%Y A377087 Cf. A376270, A376272, A377086, A377088.
%Y A377087 A193585 is the analog for happy numbers.
%K A377087 nonn,base
%O A377087 2,5
%A A377087 N. Bradley Fox, _Nathan Fox_, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024