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 A375101 #10 Jul 30 2024 15:22:07 %S A375101 1,11,112,1124,11248,112487,1124875,11248751,112487512,1124875124, %T A375101 11248751248,112487512487,1124875124875,11248751248751, %U A375101 112487512487512,1124875124875124,11248751248751248,112487512487512487,1124875124875124875,11248751248751248751,112487512487512487512 %N A375101 a(0) = 1; a(n+1) = 10*a(n) + A010888(a(n)), where A010888 = digital root. %C A375101 The digital roots of the terms are (1, 2, 4, 8, 7, 5) with cyclic repetitions. %C A375101 Initial values 2, 4, 5, 7 or 8 yield the same repeating pattern; for initial values 3 or 6 the repeating pattern is (3, 6), and for a(0) = 9 it is 9. %H A375101 Eric Angelini, <a href="https://cinquantesignes.blogspot.com/2024/07/fun-with-roots.html">Fun with roots</a>, personal blog CinquanteSignes.blogspot.com (and post to the SeqFan list), Jul 28 2024. %F A375101 a(6n) = a(6n-6)*10^6 + 124875. %e A375101 The digital root of a(0) = 1 is 1, thus a(1) = 11. %e A375101 Then, the digital root of a(1) = 11 is 2, thus a(2) = 112, etc. %o A375101 (PARI) A375101_upto(N, a=1)=vector(N, i, a+=if(i>1, 9*a+(a-1)%9+1)) %Y A375101 Cf. A010888. %K A375101 nonn,base,easy %O A375101 0,2 %A A375101 _M. F. Hasler_, Jul 30 2024