A375101 a(0) = 1; a(n+1) = 10*a(n) + A010888(a(n)), where A010888 = digital root.

1, 11, 112, 1124, 11248, 112487, 1124875, 11248751, 112487512, 1124875124, 11248751248, 112487512487, 1124875124875, 11248751248751, 112487512487512, 1124875124875124, 11248751248751248, 112487512487512487, 1124875124875124875, 11248751248751248751, 112487512487512487512

Offset: 0

Author

M. F. Hasler, Jul 30 2024

Keywords

• nonn
• base
• easy

Comments

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

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.

Examples

			The digital root of a(0) = 1 is 1, thus a(1) = 11.
Then, the digital root of a(1) = 11 is 2, thus a(2) = 112, etc.
		

Links

• Eric Angelini, Fun with roots, personal blog CinquanteSignes.blogspot.com (and post to the SeqFan list), Jul 28 2024.

Crossrefs

Cf. A010888.

Programs

PARI

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

Formula

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