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%I #20 Jan 01 2021 11:53:06
%S 0,0,1,22,343,4664,58986,713315,8367717,96022849,1083685281,
%T 12071420713,133059886145,1454055651577,15775124417009,
%U 170096923182441,1824426021947881,19478828120713394,207133960219479637,2194796392318253180,23182531824417099723
%N Number of '6' digits in the set of all numbers from 0 to A014824(n) = Sum_{i=1..n} i*10^(n-i) = (0, 1, 12, 123, 1234, 12345, ...).
%H David A. Corneth, <a href="/A277836/b277836.txt">Table of n, a(n) for n = 0..998</a>
%F a(n) = A277839(n) = A083449(n) = A277830(n) - 1 for n < 6,
%F a(n) = A277835(n) - 7*10^(n-6) for n >= 6,
%F a(n) = A277837(n) + 8*10^(n-7) for n >= 7.
%e For n=2 there is only one digit '6' in the sequence 0, 1, 2, ..., 12.
%e For n=3 there are 11 + 10 = 21 more digits '6' in { 16, 26, ..., 56, 60, ..., 69, 76, 86, ..., 116 }, where 66 accounts for two '6's.
%t T[int_Integer, {bndsLow_Integer, bndsUpp_Integer}] := Table[
%t Count[
%t Flatten[Table[
%t IntegerDigits[m],
%t {m, 1, Sum[
%t 10^i - 1,
%t {i, n}
%t ]/9
%t }
%t ]],
%t int
%t ],
%t {n, bndsLow, bndsUpp}
%t ];
%t T[6, {0, 7}](* _Robert P. P. McKone_, Jan 01 2021 *)
%o (PARI) print1(c=N=0);for(n=1,8,print1(","c+=sum(k=N+1,N=N*10+n,#select(d->d==6,digits(k)))))
%o (PARI) A277836(n,m=6)=if(n>m,A277836(n,m+1)+(m+2)*10^(n-m-1),A277830(n)-(m>n)) \\ _M. F. Hasler_, Nov 02 2016
%Y Cf. A277830 - A277838, A277849, A277635, A272525, A083449, A014824.
%K nonn,base
%O 0,4
%A _M. F. Hasler_, Nov 01 2016
%E More terms from _Lars Blomberg_, Nov 05 2016
%E Removed incorrect b-file. - _David A. Corneth_, Dec 31 2020