OFFSET
1,1
COMMENTS
Conjecture: This sequence is infinite. - Ahmad J. Masad, Feb 17 2020
Conjecture: If this sequence is infinite, then there exists a minimum sufficiently large integer k, such that for all a(n) > k, there exists a positive integer x and there exists m>n such that x(x-1) < a(n) < x^2 and x^2 < a(m) < x(x+1). This conjecture is similar to Oppermann's conjecture. - Ahmad J. Masad, Jun 23 2020
From Aitzaz Imtiaz, Sep 20 2026: (Start)
3 is the only Sophie Germain prime (A005384) in this sequence, as any Sophie Germain prime p > 3 is congruent to 2 (mod 3) and lucky numbers cannot be congruent to 2 (mod 3).
7 is the only safe prime (A005385) in this sequence, as any safe prime q > 7 is congruent to 2 (mod 3) and lucky numbers cannot be congruent to 2 (mod 3). (End)
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
Marthinus Michael Dreeckmeier, On the Fundamental Arithmetical Structure and Distribution of Lucky Numbers, arXiv:2511.11657 [math.GM], 2025. See p. 11.
Wikipedia, Lucky prime
MATHEMATICA
luckies = Range[1, 1248, 2]; i = 2; While[ i <= (len = Length@luckies) && (k = luckies[[i]]) <= len, luckies = Drop[luckies, {k, len, k}]; i++ ]; Select[luckies, PrimeQ@# &] (* Robert G. Wilson v, May 12 2006 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved
