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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

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OFFSET

0,2

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.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200

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

Index entries for linear recurrences with constant coefficients, signature (11,-10,-1,11,-10).

FORMULA

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