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A264828
Nonprimes that are not twice a prime.
11
1, 8, 9, 12, 15, 16, 18, 20, 21, 24, 25, 27, 28, 30, 32, 33, 35, 36, 39, 40, 42, 44, 45, 48, 49, 50, 51, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 77, 78, 80, 81, 84, 85, 87, 88, 90, 91, 92, 93, 95, 96, 98, 99, 100, 102, 104
OFFSET
1,2
COMMENTS
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
LINKS
N. J. A. Sloane, Table of n, a(n) for n = 1..20000 [Terms 1 to 10000 from Robert Israel.]
FORMULA
a(n) = A009188(n-2) for n>=3. - Alois P. Heinz, Oct 17 2024
MAPLE
Primes, Nonprimes:= selectremove(isprime, {$1..1000}):
sort(convert(Nonprimes minus map(`*`, Primes, 2), list)); # Robert Israel, Nov 30 2015
MATHEMATICA
Select[Range@ 104, And[! PrimeQ@ #, Or[PrimeOmega@ # != 2, OddQ@ #]] &] (* Michael De Vlieger, Nov 27 2015 *)
Select[Range@110, Nor[PrimeQ[#], PrimeQ[#/2]] &] (* Vincenzo Librandi, Jan 22 2016 *)
PROG
(PARI) print1(1, ", "); forcomposite(n=1, 1e3, if(n % 2 == 1 || !isprime(n/2), print1(n, ", "))) \\ Altug Alkan, Dec 01 2015
(Python)
from itertools import count, islice
from sympy import isprime
def A264828_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:not (isprime(n) or (n&1^1 and isprime(n>>1))), count(max(startvalue, 1)))
A264828_list = list(islice(A264828_gen(), 20)) # Chai Wah Wu, Mar 26 2024
(Python)
from sympy import primepi
def A264828(n):
def f(x): return int(n+primepi(x)+primepi(x>>1))
m, k = n, f(n)
while m != k: m, k = k, f(k)
return m # Chai Wah Wu, Oct 17 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Nov 26 2015
STATUS
approved