|
%I #56 Mar 26 2024 12:56:22
%S 1,8,9,12,15,16,18,20,21,24,25,27,28,30,32,33,35,36,39,40,42,44,45,48,
%T 49,50,51,52,54,55,56,57,60,63,64,65,66,68,69,70,72,75,76,77,78,80,81,
%U 84,85,87,88,90,91,92,93,95,96,98,99,100,102,104
%N Nonprimes that are not twice a prime.
%C Except for the initial 1, if n is in the sequence, so is k*n for all k > 1. So the odd semiprimes (A046315) and numbers of the form 4*p (A001749) where p is prime are core subsequences which give the initial terms of arithmetic progressions in this sequence. - _Altug Alkan_, Nov 29 2015
%H N. J. A. Sloane, <a href="/A264828/b264828.txt">Table of n, a(n) for n = 1..20000</a> [Terms 1 to 10000 from _Robert Israel_.]
%p Primes, Nonprimes:= selectremove(isprime, {$1..1000}):
%p sort(convert(Nonprimes minus map(`*`,Primes,2),list)); # _Robert Israel_, Nov 30 2015
%t Select[Range@ 104, And[! PrimeQ@ #, Or[PrimeOmega@ # != 2, OddQ@ #]] &] (* _Michael De Vlieger_, Nov 27 2015 *)
%t Select[Range@110, Nor[PrimeQ[#], PrimeQ[#/2]] &] (* _Vincenzo Librandi_, Jan 22 2016 *)
%o (PARI) print1(1, ", "); forcomposite(n=1, 1e3, if(n % 2 == 1 || !isprime(n/2), print1(n, ", "))) \\ _Altug Alkan_, Dec 01 2015
%o (Python)
%o from itertools import count, islice
%o from sympy import isprime
%o def A264828_gen(startvalue=1): # generator of terms >= startvalue
%o return filter(lambda n:not (isprime(n) or (n&1^1 and isprime(n>>1))),count(max(startvalue,1)))
%o A264828_list = list(islice(A264828_gen(),20)) # _Chai Wah Wu_, Mar 26 2024
%Y Cf. A009188, A018252, A100484.
%K nonn,easy
%O 1,2
%A _Giovanni Teofilatto_, Nov 26 2015
|
