This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A175402 #11 Jan 03 2021 01:00:20
%S A175402 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,2,3,4,1,1,1,3,
%T A175402 2,3,3,3,3,2,1,1,2,3,3,2,2,2,3,3,1,1,3,2,3,3,2,3,2,2,1,1,4,4,2,3,3,3,
%U A175402 2,2,1,1,4,4,2,2,2,3,2,2,1,1,3,4,2,3,3,2,2,2,1,1,2,3,3,2,3,3,2,2,1,1,1,1,1,1,1,1
%N A175402 a(n) is the number of iterations of {r -> (((D_1^D_2)^D_3)^...)^D_k, where D_k is the k-th decimal digit of r} needed to reach a one-digit number, starting at r = n.
%C A175402 Conjecture: max(a(n)) = 4.
%C A175402 Assuming that A020665(2) = 86, A020665(3) = 68, A020665(5) = 58, and A020665(7) = 35, this conjecture is true, since in that case the largest power of a decimal digit that has no 0 is 7^35, and of those powers p none have a(p) > 3. The only n for which a(n) = 4 are those where one iteration goes to 6^2, 7^2, 6^3, 7^3, or 2^9.
%e A175402 For n = 29: a(29) = 4 because for the number 29 there are 4 steps of defined iteration: {2^9 = 512}, {(5^1)^2 = 25}, {2^5 = 32}, {3^2 = 9}.
%o A175402 (PARI) iter(n)=my(v=eval(Vec(Str(n))));v[1]^prod(i=2,#v,v[i])
%o A175402 a(n)=my(k=0);while(n>9,k++;n=iter(n));k
%Y A175402 Cf. A175398, A175399, A175400, A175401, A175403, A175405.
%K A175402 nonn,base
%O A175402 0,25
%A A175402 _Jaroslav Krizek_, May 01 2010
%E A175402 Corrected, extended, comment, and program from _Charles R Greathouse IV_, Aug 03 2010