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 A352301 #46 May 11 2022 10:33:50
%S A352301 7,2,7,3,7,6,7,5,8,2,3,6,8,0,3,0,5,1,6,0,0,4,4,2,5,3,1,0,0,0,1,8,4,2,
%T A352301 3,1,7,2,8,6,1,9,9,0,3,6,9,7,4,1,1,9,5,4,8,7,6,7,2,2,2,7,5,7,6,5,5,6,
%U A352301 0,0,3,9,8,7,6,3,8,2,3,4,7,2,2,4,4,7
%N A352301 a(n) is the n-th-to-last digit of A007013(n + 1).
%C A352301 Although the sequences for the most significant digits of Mersenne numbers, A000225, are not cyclic (the most significant is not cyclic, the second most is not, etc.), the sequences for the least significant digits are. For example, if p == 3 (mod 4), then A000225(p) == 7 (mod 10). Since A007013(n + 1) = A000225(A007013(n)) and A007013(1) == 3 (mod 4), all subsequent values will be congruent to 7 (mod 10). Similarly, if p == 7 (mod 20), A000225(p) == 27 (mod 100). In general, if p == x (mod A005054(n)), then A000225(p) == A000225(x) (mod 10^n).
%C A352301 There are many primes of the form Sum_{i=1..n} a(i)*10^(i - 1). The largest known is for n = 7032 (it is 7032 digits long).
%H A352301 Davis Smith, <a href="/A352301/b352301.txt">Table of n, a(n) for n = 1..7032</a>
%F A352301 a(n) = floor(A007013(n + 1)/(10^(n - 1))) (mod 10).
%F A352301 A007013(n + 1) == Sum_{i=1..n} a(i)*10^(i - 1) (mod 10^n).
%o A352301 (PARI) A352301_vec(n)=my(N=7,m=0);while(m<n,m++;N=lift(Mod(2,10^m)^N)-1);Vecrev(digits(N))
%Y A352301 Cf. A000225, A005054, A007013.
%K A352301 nonn,base,easy
%O A352301 1,1
%A A352301 _Davis Smith_, Mar 11 2022