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%I #32 Jan 01 2021 11:51:05
%S 0,0,2,27,389,5121,63553,758985,8824417,100589849,1129355281,
%T 12528120713,137626886149,1499725651622,16231824417465,
%U 174663923187008,1870096021993551,19935528121170094,211700960224046637,2240466392363923180,23639231824873799723
%N Number of '2' 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="/A277832/b277832.txt">Table of n, a(n) for n = 0..998</a>
%F a(n) = A277831(n) - 3*10^(n-2) [for n >= 2] = A277833(n) + 4*10^(n-3) [n >= 3].
%F More generally, for m = 0, ..., 9, let a[m] denote A277830, ..., A277838 and A277849, respectively. Then a[0](n) = a[n](n) = a[m](n) + 1 for all m > n >= 0, and a[m-1](n) = a[m](n) + (m+1)*10^(n-m) for all n >= m > 1.
%e For n=2 are counted the two '2's in { 2, 12 }.
%t Array[Total@ DigitCount[Range[Sum[10^i - 1, {i, #}]/9], 10, 2] &, 7] (* _Michael De Vlieger_, Dec 31 2020 *)
%o (PARI) print1(c=N=0);for(n=1,8,print1(","c+=sum(k=N+1,N=N*10+n,#select(d->d==2,digits(k)))))
%o (PARI) A277832(n)=if(n<3,(n==2)*2, n<13,A277833(n)+4*10^(n-3), error("n > 12 not yet implemented")) \\ _M. F. Hasler_, Nov 02 2016, edited Dec 28 2020
%o (PARI) a(n) = {if(n == 0, return(0)); n = (10^(n+1)\9-n)\9; f(n, 2) }
%o f(n, {c = 2}) = { my(d = digits(n), res = 0); for(i = 1, #d - 1, res += d[i] * (#d - i)*10^(#d - i - 1); if(d[i]==c, res+=(n % (10^(#d - i)) + 1); ); if(d[i] > c, res+=(10^(#d - i)) ); ); if(d[#d] >= c, res++); res } \\ _David A. Corneth_, Dec 31 2020
%Y Cf. A102685, A277830 - A277838, A277849, A277635, A272525, A083449, A014824.
%K nonn,base
%O 0,3
%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