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A247107 a(0) = 0, a(n) = previous term + repunit of length of previous term for n > 0. 1
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, 220, 331, 442, 553, 664, 775, 886, 997, 1108, 2219, 3330, 4441, 5552, 6663, 7774, 8885, 9996, 11107, 22218, 33329, 44440, 55551, 66662, 77773, 88884, 99995, 111106, 222217, 333328, 444439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(0) = 0, a(n) = a(n-1) + A002275(A055642(a(n-1))) for n>0.

From Jon E. Schoenfield, Nov 30 2014: (Start)

For n > 1, a(n) = a(n-1) + (10^(floor(log_10(a(n-1))) + 1) - 1) / 9.

For n > 0, a(n) = ((n-1) mod 9 + 1) * (10^D - 1) / 9 + 1 - D, where D = floor((n-1)/9) + 1. (There are exactly D digits in a(n).) (End)

G.f.: -(10*x^10-10*x^9+1)*x/((10*x^9-1)*(x-1)^2). - Alois P. Heinz, Nov 30 2014

EXAMPLE

98 = 9*10 + 8 -> 10*10 + 9 = 109.

109 = 1*100 + 0*10 + 9*1 -> 2*100 + 1*10 + 10*1 = 220.

a(42) = 44440 + (10^(floor(log_10(44440))+1)-1) / 9 = 44440 + (10^(4+1)-1) / 9 = 44440 + 99999/9 = 44440 + 11111 = 55551.

CROSSREFS

Similar to A158699, but with simpler rules.

Cf. A002275, A055642.

Sequence in context: A331975 A068860 A158699 * A061511 A138142 A085890

Adjacent sequences:  A247104 A247105 A247106 * A247108 A247109 A247110

KEYWORD

nonn,base,easy

AUTHOR

Dhilan Lahoti, Nov 30 2014

STATUS

approved

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Last modified May 12 13:02 EDT 2021. Contains 343823 sequences. (Running on oeis4.)