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A031157 Numbers that are both lucky and prime. 22
3, 7, 13, 31, 37, 43, 67, 73, 79, 127, 151, 163, 193, 211, 223, 241, 283, 307, 331, 349, 367, 409, 421, 433, 463, 487, 541, 577, 601, 613, 619, 631, 643, 673, 727, 739, 769, 787, 823, 883, 937, 991, 997, 1009, 1021, 1039, 1087, 1093, 1117, 1123 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
A010051(a(n))*A145649(a(n)) = 1. - Reinhard Zumkeller, Oct 19 2008
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
LINKS
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
Sequence in context: A249378 A136060 A023227 * A049488 A136051 A100750
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)