We know that "There exist some real k such that ∀ integer n>1 the integer part of k∗nln(n) is always prime?" is false (prove here Is there a $k$ for which $k\cdot n\ln n$ takes only prime values? ) But and if we just consider the odd numbers generated by the function then the same question: Does it exist any k for the same but just consider the odd? (Sorry for my english level)
2026-04-17 20:47:22.1776458842
Second part of Eloi's Conjecture
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No, because we can extend the proof to show that there are numbers divisible by 3, 5, etc. In fact, for any choice of $w\in\mathbb{Z}^+,$ there are infinitely many numbers in the generated sequence which are divisible by any given $w$.