cp's OEIS Frontend

A377088 Number of attractors 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 A377088 #7 Oct 16 2024 20:56:18
%S A377088 1,5,2,3,8,6,11,4,16,14,23,18,42,7,24,34,26,58,98,51,99,88,51,57,103,
%T A377088 72,89,60,69,35,78,146,39,90,73,11,109,113,71,156,220,93,176,101,132,
%U A377088 172,187,10,160,95,221,226,69,55,163,110,137,287,168,69,260,194,208
%N A377088 Number of attractors 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 A377088 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 A377088 Nathan Fox, <a href="/A377088/b377088.txt">Table of n, a(n) for n = 2..100</a>
%H A377088 N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.
%e A377088 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, one 3-cycle, one 4-cycle, and one 7-cycle. Therefore a(10) = 1 + 1 + 3 + 4 + 7 = 16.
%Y A377088 Cf. A376270, A376272, A377086, A377087.
%Y A377088 A193586 is the analog for happy numbers.
%K A377088 nonn,base
%O A377088 2,2
%A A377088 N. Bradley Fox, _Nathan Fox_, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024