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%I #48 Aug 07 2020 23:38:02
%S 3,7,13,31,37,43,67,73,79,127,151,163,193,211,223,241,283,307,331,349,
%T 367,409,421,433,463,487,541,577,601,613,619,631,643,673,727,739,769,
%U 787,823,883,937,991,997,1009,1021,1039,1087,1093,1117,1123
%N Numbers that are both lucky and prime.
%C A010051(a(n))*A145649(a(n)) = 1. - _Reinhard Zumkeller_, Oct 19 2008
%C Conjecture: This sequence is infinite. - _Ahmad J. Masad_, Feb 17 2020
%C 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
%H T. D. Noe, <a href="/A031157/b031157.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lucky_number#Lucky_primes">Lucky prime</a>
%t 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 *)
%Y Cf. A000959, A055728.
%K nonn
%O 1,1
%A _Patrick De Geest_
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