cp's OEIS Frontend

A175403 a(n) is the smallest number m requiring n iterations {((((D_1^D_2)^D_3)^D_4)^...)^D_k to reach a one-digit number starting at r = n, where D_k is the k-th digit D of the number r and k is the digit number of the number r in the decimal expansion of r (A055642)}.

%I A175403 #12 Jan 15 2021 21:18:37
%S A175403 0,10,24,26,29
%N A175403 a(n) is the smallest number m requiring n iterations {((((D_1^D_2)^D_3)^D_4)^...)^D_k to reach a one-digit number starting at r = n, where D_k is the k-th digit D of the number r and k is the digit number of the number r in the decimal expansion of r (A055642)}.
%C A175403 Conjecture: sequence is finite.
%C A175403 Assuming that A020665(2) = 86, A020665(3) = 68, A020665(5) = 58 and A020665(7) = 35, a(4) is the last term; see A175402.
%e A175403 For n = 4: a(4) = 29 because 29 is the smallest number with 4 steps of defined iteration: {2^9 = 512}, {(5^1)^2 = 25}, {2^5 = 32}, {3^2 = 9}.
%Y A175403 Cf. A020665, A175398, A175399, A175400, A175401, A175402, A175405.
%K A175403 nonn,base,more
%O A175403 0,2
%A A175403 _Jaroslav Krizek_, May 01 2010
%E A175403 Comment and edits from _Charles R Greathouse IV_, Aug 03 2010
%E A175403 Further edits from _N. J. A. Sloane_, Aug 08 2010. I am still worried that n is mentioned too many times in the definition.