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A199593 Numbers n such that 3n-2, 3n-1 and 3n are all composite. 3
9, 12, 17, 19, 22, 26, 29, 31, 32, 39, 40, 41, 42, 45, 48, 49, 52, 54, 57, 59, 62, 63, 68, 69, 70, 72, 73, 74, 79, 82, 83, 85, 87, 89, 92, 96, 97, 99, 100, 101, 102, 107, 108, 109, 110, 112, 114, 115, 119, 121, 122, 124, 126, 129, 131, 132, 135, 136, 138, 139, 142, 143, 146, 149, 151, 152, 157, 158, 159, 161, 162, 165, 166, 169, 171, 172, 173, 176, 177, 178 (list; graph; refs; listen; history; text; internal format)
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

Bogart B. Strauss, Formula Explanation, pp. 1, 2, 3.

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

CROSSREFS

Cf. A053726, A199595, A001222, A007310, A075743, A084967, A249823.

Sequence in context: A176062 A027571 A154631 * A174525 A141552 A317720

Adjacent sequences:  A199590 A199591 A199592 * A199594 A199595 A199596

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Nov 08 2011

STATUS

approved

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Last modified October 22 18:44 EDT 2019. Contains 328319 sequences. (Running on oeis4.)