cp's OEIS Frontend

A377086 Number of fixed points 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 A377086 #7 Oct 16 2024 20:54:34
%S A377086 1,2,2,1,1,4,3,4,2,3,1,3,5,2,4,4,2,4,1,3,3,3,1,5,2,3,5,4,4,9,2,1,1,4,
%T A377086 2,6,4,1,2,5,3,6,3,1,2,3,1,7,2,1,3,3,1,5,4,6,5,4,2,8,3,2,7,3,1,4,4,2,
%U A377086 3,6,3,9,2,3,4,9,3,7,3,2,6,5,1,7,3,3,3
%N A377086 Number of fixed points 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 A377086 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).
%C A377086 Unlike the related sequence A193583, which contains only odd numbers, this sequence contains even numbers and odd numbers.
%H A377086 Nathan Fox, <a href="/A377086/b377086.txt">Table of n, a(n) for n = 2..100</a>
%H A377086 N. Bradley Fox et al., <a href="https://arxiv.org/abs/2409.09863">Elated Numbers</a>, arXiv:2409.09863 [math.NT], 2024.
%e A377086 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) = 2.
%Y A377086 Cf. A376270, A376272, A377087, A377088.
%Y A377086 A193583 is the analog for happy numbers.
%K A377086 nonn,base
%O A377086 2,2
%A A377086 N. Bradley Fox, _Nathan Fox_, Helen Grundman, Rachel Lynn, Changningphaabi Namoijam, Mary Vanderschoot, Oct 15 2024