A375101 - OEIS

%I #10 Jul 30 2024 15:22:07

%S 1,11,112,1124,11248,112487,1124875,11248751,112487512,1124875124,

%T 11248751248,112487512487,1124875124875,11248751248751,

%U 112487512487512,1124875124875124,11248751248751248,112487512487512487,1124875124875124875,11248751248751248751,112487512487512487512

%N a(0) = 1; a(n+1) = 10*a(n) + A010888(a(n)), where A010888 = digital root.

%C The digital roots of the terms are (1, 2, 4, 8, 7, 5) with cyclic repetitions.

%C 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 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 a(6n) = a(6n-6)*10^6 + 124875.

%e The digital root of a(0) = 1 is 1, thus a(1) = 11.

%e Then, the digital root of a(1) = 11 is 2, thus a(2) = 112, etc.

%o (PARI) A375101_upto(N, a=1)=vector(N, i, a+=if(i>1, 9*a+(a-1)%9+1))

%Y Cf. A010888.

%K nonn,base,easy

%O 0,2

%A _M. F. Hasler_, Jul 30 2024