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A306567 a(n) is the largest value obtained by iterating x -> noz(x + n) starting from 0 (where noz(k) = A004719(k) omits the zeros from k). 2
9, 99, 27, 99, 96, 99, 63, 99, 81, 91, 99, 195, 94, 295, 93, 291, 113, 189, 171, 992, 159, 187, 187, 483, 988, 475, 153, 281, 181, 273, 279, 577, 297, 997, 567, 369, 333, 363, 351, 994, 219, 465, 357, 663, 459, 461, 423, 192, 441, 965, 399, 999, 437, 126, 551 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For any n > 0, a(n) is well defined:

- the set of zeroless numbers (A052382) contains arbitrarily large gaps,

- for example, for any k > 0, the interval I_k = [10^k..(10^(k+1)-1)/9-1] if free of zeroless numbers,

- let i be such that #I_i > n,

- let b_n be defined by b_n(0) = 0, and for any j > 0, b_n(j) = noz(b_n(j-1) + n),

- as b_n starts below 10^i and cannot cross the gap constituted by I_i,

- b_n is bounded (and eventually periodic), QED.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program for A306567

FORMULA

Empirically, for any k >= 0:

- a(    10^k) =  9 * 10^k +     (10^k-1)/9,

- a(2 * 10^k) = 99 * 10^k + 2 * (10^k-1)/9,

- a(3 * 10^k) = 27 * 10^k + 3 * (10^k-1)/9,

- a(4 * 10^k) = 99 * 10^k + 4 * (10^k-1)/9,

- a(5 * 10^k) = 96 * 10^k + 5 * (10^k-1)/9,

- a(6 * 10^k) = 99 * 10^k + 6 * (10^k-1)/9,

- a(7 * 10^k) = 63 * 10^k + 7 * (10^k-1)/9,

- a(8 * 10^k) = 99 * 10^k + 8 * (10^k-1)/9,

- a(9 * 10^k) = 81 * 10^k + 9 * (10^k-1)/9.

EXAMPLE

For n = 1:

- noz(0 + 1) = 1,

- noz(1 + 1) = 2,

- noz(2 + 1) = 3,

  ...

- noz(7 + 1) = 8,

- noz(8 + 1) = 9,

- noz(9 + 1) = noz(10) = 1,

- hence a(1) = 9.

PROG

See Links section.

CROSSREFS

See A306569 for the multiplicative variant.

Cf. A004719, A052382.

Sequence in context: A066557 A289214 A121706 * A061817 A083835 A305670

Adjacent sequences:  A306564 A306565 A306566 * A306568 A306569 A306570

KEYWORD

nonn,look,base

AUTHOR

Rémy Sigrist, Feb 24 2019

STATUS

approved

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Last modified February 19 13:03 EST 2020. Contains 332044 sequences. (Running on oeis4.)