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A331163 a(n) is the number of occurrences of the most frequently seen difference between adjacent digits in the concatenation of a(0) to a(n-1), with a(0) = 0, a(1) = 0.

%I A331163 #13 Jan 16 2020 13:12:24
%S A331163 0,0,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,10,10,12,14,15,15,15,15,15,
%T A331163 15,15,15,15,17,18,18,18,18,18,18,18,18,18,18,19,20,21,21,21,21,22,23,
%U A331163 24,25,25,25,25,25,25,25,25,25,25,25,25,25,27,28,28,28,28,28,28,28,28,28,28,28,28,28,28,29,30,31,31,31,31,31
%N A331163 a(n) is the number of occurrences of the most frequently seen difference between adjacent digits in the concatenation of a(0) to a(n-1), with a(0) = 0, a(1) = 0.
%C A331163 In the first 10 million terms the most frequently seen digit difference is 1, which leads other digit difference counts for 2589052 terms. The least seen is 9, which only holds the lead for 990 terms and does not become the most frequently seen digit difference until a(23521), after a run of 1228 consecutive terms of 9090. The longest series of unchanging terms begins at a(7727945) = 7040480 which begins a run of 94553 consecutive terms of 7040480.
%H A331163 Robert Israel, <a href="/A331163/b331163.txt">Table of n, a(n) for n = 0..10000</a>
%e A331163 a(2) = 1 as the concatenation of a(0) and a(1) = '00', and the only adjacent digit difference in '00' is 0, and that difference has occurred one time.
%e A331163 a(3) = 1 as the adjacent digit differences in '001' are 0 and 1, both of which have occurred one time.
%e A331163 a(4) = 2 as '0011' contains two pairs of adjacent digits which differ by 0.
%e A331163 a(22) = 12 as '001122334455667788991010' contains twelve pairs of adjacent digits which differ by 1.
%p A331163 DC:= [0]: last:= 0:
%p A331163 Res:= 0,0:
%p A331163 Ct:= Array(0..9):
%p A331163 Ct[0]:= 1:
%p A331163 for n from 2 to 100 do
%p A331163   v:= max(Ct);
%p A331163   Res:= Res, v;
%p A331163   L:= [last,op(ListTools:-Reverse(convert(v,base,10)))];
%p A331163   DL:= map(abs,L[2..-1]-L[1..-2]);
%p A331163   last:= L[-1];
%p A331163   for i from 1 to nops(DL) do
%p A331163     Ct[DL[i]]:= Ct[DL[i]]+1
%p A331163   od;
%p A331163 od:
%p A331163 Res; # _Robert Israel_, Jan 16 2020
%Y A331163 Cf. A040115.
%K A331163 nonn,base
%O A331163 0,5
%A A331163 _Scott R. Shannon_, Jan 11 2020