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A102644 A006530(x)=2 is a local minimum if x=2^n. Running downward with argument x started at 2^n, the largest prime divisor should increase. The value of first peak is a(n).

%I A102644 #10 Aug 01 2017 02:52:51
%S A102644 2,3,7,13,31,61,127,127,73,1021,89,4093,8191,16381,151,257,131071,
%T A102644 131071,524287,1048573,337,683,178481,16777213,1801,8191,262657,
%U A102644 1877171,2089,46684427,2147483647,2147483647,599479,3360037,6871947673,283007
%N A102644 A006530(x)=2 is a local minimum if x=2^n. Running downward with argument x started at 2^n, the largest prime divisor should increase. The value of first peak is a(n).
%C A102644 We may call these terms "downward-zenith-primes" belonging to 2^n-s. They do not exceed previous-primes before 2^n [A014234(n)].
%H A102644 Michael De Vlieger, <a href="/A102644/b102644.txt">Table of n, a(n) for n = 1..150</a>
%e A102644 n=20: 2^20=1048576; the largest prime divisors for arguments if running downward from 2^20 are as follows: {2,41,524287,1048573,73}.
%e A102644 The first lower peak before argument 2^20=1048576 is a(20)=1048573.
%e A102644 n=1: a(1)=2 the peak equals the central value because there are no prime divisors>0 below n=2^1=2.
%t A102644 Table[2 + Total@ TakeWhile[Differences@ Map[FactorInteger[#][[-1, 1]] &,
%t A102644 TakeWhile[Range[2^n, 2^n - 20, -1], # > 0 &]], # > 0 &], {n, 36}] (* _Michael De Vlieger_, Jul 31 2017 *)
%Y A102644 Cf. A006530, A102640, A102641, A102642, A102643, A014234.
%K A102644 nonn
%O A102644 1,1
%A A102644 _Labos Elemer_, Jan 21 2005