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Empirical observation of the available list shows that every positive integer of the form 99*k-2 such that 1 < k < 9 belongs to the sequence; every positive integer of the form 999*k-1 such that 1 < k < 9 belongs to the sequence except for k=5, which is a palindromic number; every positive integer of the form 9999*k such that 1 < k < 9 belongs to the sequence, and 99999*2+1 belongs to the sequence. Thus, it can be conjectured that every positive integer n in base 10 of the form 999...9*k-m, such that 1 < k < 9, m = 4-j, and j > 1, where j is the number of 9's composing the form of n, is either a palindromic number or belongs to this sequence. - Juan Moreno Borrallo, Aug 10 2020

As pointed out by @Mathlove on Mathematics Stack Exchange (see Links section), the above conjecture can be improved to conjecture that some positive integer n in base 10 such that n = (10^j-1)*k - (4-j) and 2 + (j-5)*floor(j/6) <= k <= j + 6 + floor(j/4) is either a palindromic number or belongs to this sequence. - Juan Moreno Borrallo, Mar 15 2021

Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/3789543/observation-and-conjecture-on-lychrel-numbers">Observation and conjecture on Lychrel numbers</a>

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As pointed out by @Mathlove in MathStackExchange on Mathematics Stack Exchange (see Links section), the above conjecture can be improved to conjecture that some positive integer n in base 10 such that n = (10^j-1)*k - (4-j) and 2 + (j-5)*floor(j/6) <= k <= j + 6 + floor(j/4) is either a palindromic number or belongs to this sequence. - Juan Moreno Borrallo, Mar 15 2021

MathStackExchange, Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/3789543/observation-and-conjecture-on-lychrel-numbers">Observation and conjecture on Lychrel numbers</a>

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