A377088 - OEIS

%I #7 Oct 16 2024 20:56:18

%S 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 72,89,60,69,35,78,146,39,90,73,11,109,113,71,156,220,93,176,101,132,

%U 172,187,10,160,95,221,226,69,55,163,110,137,287,168,69,260,194,208

%N 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 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 Nathan Fox, <a href="/A377088/b377088.txt">Table of n, a(n) for n = 2..100</a>

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

%e 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 Cf. A376270, A376272, A377086, A377087.

%Y A193586 is the analog for happy numbers.

%K nonn,base

%O 2,2

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