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URL: https://oeis.org/A375101

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A375101
a(0) = 1; a(n+1) = 10*a(n) + A010888(a(n)), where A010888 = digital root.
1
1, 11, 112, 1124, 11248, 112487, 1124875, 11248751, 112487512, 1124875124, 11248751248, 112487512487, 1124875124875, 11248751248751, 112487512487512, 1124875124875124, 11248751248751248, 112487512487512487, 1124875124875124875, 11248751248751248751, 112487512487512487512
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
Eric Angelini, Fun with roots, personal blog CinquanteSignes.blogspot.com (and post to the SeqFan list), Jul 28 2024.
FORMULA
a(6*n) = a(6*n-6)*10^6 + 124875.
G.f.: (1 + x^2 + 3*x^3 + 4*x^4)/((1 - x)*(1 + x)*(1 - 10*x)*(1 - x + x^2)). - Andrew Howroyd, Nov 13 2025
EXAMPLE
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.
MATHEMATICA
NestList[10*# + Mod[#-1, 9] + 1 &, 1, 20] (* Paolo Xausa, Jan 19 2026 *)
PROG
(PARI) A375101_upto(N, a=1)=vector(N, i, a+=if(i>1, 9*a+(a-1)%9+1))
CROSSREFS
Cf. A010888.
Sequence in context: A094704 A019523 A359143 * A361350 A361501 A372074
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Jul 30 2024
STATUS
approved