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A059456 Unsafe primes: primes not in A005385.

%I A059456 #22 Dec 29 2024 21:18:40
%S A059456 2,3,13,17,19,29,31,37,41,43,53,61,67,71,73,79,89,97,101,103,109,113,
%T A059456 127,131,137,139,149,151,157,163,173,181,191,193,197,199,211,223,229,
%U A059456 233,239,241,251,257,269,271,277,281,283,293,307,311,313,317,331,337
%N A059456 Unsafe primes: primes not in A005385.
%C A059456 A010051(a(n))*(1-A156659(a(n))) = 1; subsequence of A156657. - _Reinhard Zumkeller_, Feb 18 2009
%C A059456 Also, primes p such that p-1 is a non-semiprime. - _Juri-Stepan Gerasimov_, Apr 28 2010
%C A059456 Conjecture: From the sequence of prime numbers, let 2 and remove the first data iteration of 2*p+1; leave 3 and remove the prime data by the iteration 2*p+1 and we get the sequence. Example for p=2, remove(5,11,23,47); p=3, remove(7); p=13, p=17, p=19, p=23, remove(47); and so on. - _Vincenzo Librandi_, Aug 07 2010
%H A059456 Michael De Vlieger, <a href="/A059456/b059456.txt">Table of n, a(n) for n = 1..10000</a>
%F A059456 a(n) ~ n log n. - _Charles R Greathouse IV_, Dec 29 2024
%e A059456 31 is here because (31-1)/2=15 is not prime. 2 and 3 are here because 1/2 and 1 are not prime numbers.
%t A059456 Complement[Prime@ Range@ PrimePi@ Max@ #, #] &@ Select[Prime@ Range@ 90, PrimeQ[(# - 1)/2] &] (* _Michael De Vlieger_, May 01 2016 *)
%t A059456 Select[Prime[Range[100]],PrimeOmega[#-1]!=2&] (* _Harvey P. Dale_, May 13 2018 *)
%o A059456 (PARI) is(n)=isprime(n) && !isprime(n\2) \\ _Charles R Greathouse IV_, May 02 2016
%Y A059456 Cf. A005384, A005385, A053176, A059452-A059456, A007700, A005602, A023272, A023302, A023330.
%Y A059456 Initial terms for groups in A075712.
%K A059456 nonn
%O A059456 1,1
%A A059456 _Labos Elemer_, Feb 02 2001