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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.)