OFFSET
1,1
COMMENTS
From Antti Karttunen, Apr 17 2015: (Start)
Other, equivalent definitions:
Numbers n such that A007310(n) is composite, from which it follows that the function c(1) = 0, c(n) = 1-A075743(n-1) is the characteristic function of this sequence.
Numbers n such that A084967(n) has at least three prime factors (when counted with bigomega, A001222).
Numbers n such that A249823(n) is composite.
(End)
There are n - pi(3n) + 1 terms in this sequence up to n; with an efficient algorithm for pi(x) this allows isolated large values to be computed. Using David Baugh and Kim Walisch's calculation that pi(10^27) = 16352460426841680446427399 one can see that a(316980872906491652886905934) = 333333333333333333333333333 (since 999999999999999999999999997 is composite). - Charles R Greathouse IV, Sep 13 2016
REFERENCES
Ernest V. Miliauskas, letter to N. J. A. Sloane, Dec 21 1985.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
FORMULA
((1+(-1)^k)((-1)^n)(2n+3)+2k(6n+9+(-1)^n)+((-1)^k)+(12n^2)+36n+29)/4 n,k are all natural numbers and zero. - Bogart B. Strauss, Jul 10 2013
a(n) = n + 3n/log n + o(n/log n). - Charles R Greathouse IV, Oct 27 2013, corrected Aug 07 2016
MAPLE
remove(t -> isprime(3*t-1 - (t mod 2)), {$2..2000}); # Robert Israel, Apr 17 2015
MATHEMATICA
Select[Range[200], Union[PrimeQ[{3# - 2, 3# - 1, 3#}]] == {False} &] (* Alonso del Arte, Jul 06 2013 *)
PROG
(PARI) is(n)=!isprime(bitor(3*n-2, 1)) && n>1 \\ Charles R Greathouse IV, Oct 27 2013
(Scheme, after Greathouse's PARI-program above, requiring also Antti Karttunen's IntSeq-library)
(define A199593 (MATCHING-POS 1 2 (lambda (n) (not (prime? (A003986bi (+ n n n -2) 1)))))) ;; A003986bi implements binary inclusive or (A003986).
;; Antti Karttunen, Apr 17 2015
(Magma) [n: n in [1..200] | not IsPrime(3*n) and not IsPrime(3*n-1) and not IsPrime(3*n-2)]; // Vincenzo Librandi, Apr 18 2015
(Python)
from sympy import isprime
def ok(n): return n > 0 and not any(isprime(3*n-i) for i in [2, 1, 0])
print([k for k in range(179) if ok(k)]) # Michael S. Branicky, Apr 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 08 2011
STATUS
approved