This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A277837 #21 Jan 01 2021 11:53:33
%S A277837 0,0,1,22,343,4664,58985,713307,8367637,96022049,1083677281,
%T A277837 12071340713,133059086145,1454047651577,15775044417009,
%U A277837 170096123182441,1824418021947873,19478748120713314,207133160219478837,2194788392318245180,23182451824417019723
%N A277837 Number of '7' 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, ...).
%C A277837 This sequence is very similar (actually equal, for 1 <= n <= 9) to A277635, which was the original motivation for considering the family A277830 - A277838 and A277849. The main difference is that A277635 is based on A007908 (where 123456789 is followed by 12345678910) while this family is based on A014824, starts as the latter at offset 0, and therefore has a strongly different growth for n > 9.
%H A277837 David A. Corneth, <a href="/A277837/b277837.txt">Table of n, a(n) for n = 0..998</a>
%F A277837 a(n) = A277849(n) = A083449(n) = A277830(n) - 1 for n < 7,
%F A277837 a(n) = A277836(n) - 8*10^(n-7) [for n >= 7] = A277838(n) + 9*10^(n-8) [for n >= 8].
%F A277837 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 A277837 For n=2 there is only one digit '7' in the sequence 0, 1, 2, ..., 12.
%e A277837 For n=3 there are 11 + 10 = 21 more digits '7' in { 17, 27, ..., 67, 70, ..., 79, 87, 97, 107, 117 }, where 77 accounts for two '7's.
%o A277837 (PARI) print1(c=N=0);for(n=1,8,print1(","c+=sum(k=N+1,N=N*10+n,#select(d->d==7,digits(k)))))
%o A277837 (PARI) A277837(n,m=7)=if(n>16,error("n>16 not yet implemented"), n>m,A277837(n,m+1)+(m+2)*10^(n-m-1),(9*n-11)*(10^n+1)\729+2-(m>n)) \\ Edited by _M. F. Hasler_, Dec 29 2020
%Y A277837 Cf. A277830 - A277838, A277849, A277635, A272525, A083449, A014824.
%K A277837 nonn,base
%O A277837 0,4
%A A277837 _M. F. Hasler_, Nov 01 2016
%E A277837 More terms from _Lars Blomberg_, Nov 05 2016
%E A277837 Removed incorrect b-file. - _David A. Corneth_, Dec 31 2020