

A067611


Numbers of the form 6xy + x + y, where x, y are positive integers.


9



4, 6, 8, 9, 11, 13, 14, 15, 16, 19, 20, 21, 22, 24, 26, 27, 28, 29, 31, 34, 35, 36, 37, 39, 41, 42, 43, 44, 46, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 88, 89, 90, 91, 92, 93, 94
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OFFSET

1,1


COMMENTS

Equivalently, numbers n such that either 6n1 or 6n+1 is composite (or both are).
Numbers k such that 36k^21 is not a product of twin primes.  Artur Jasinski, Dec 12 2007
Apart from initial zero, union of A046953 and A046954.  Reinhard Zumkeller, Jul 13 2014
From Bob Selcoe, Nov 18 2014: (Start)
Complementary sequence to A002822.
For all k >= 1, a(n) are the only positive numbers congruent to the following residue classes:
f == k mod (6k+1);
g == (5k1) mod (6k1);
h == (5k+1) mod (6k+1).
All numbers in classes g and h will be in this sequence; for class f, the quotient must be >= 1.
When determining which numbers are contained in this sequence, it is only necessary to evaluate f, g and h when the moduli are prime and the dividends are >= 2k(3k1) (i.e., A033579(k)).
(End)
From Jason Kimberley, Oct 14 2015: (Start)
Numbers n such that A001222(A136017(n)) > 2.
The disjoint union of A060461, A121763, and A121765.
(End)


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000


EXAMPLE

4 = 6ab  a  b with a = 1, b = 1.
6 = 6ab + a  b or 6ab  a + b with a = 1, b = 1.
5 cannot be obtained by any values of a and b in 6ab  a  b, 6ab  a + b, 6ab + a  b or 6ab + a + b.


MAPLE

filter:= n > not isprime(6*n+1) or not isprime(6*n1):
select(filter, [$1..1000]); # Robert Israel, Nov 18 2014


MATHEMATICA

Select[Range[100], !PrimeQ[6#  1]  !PrimeQ[6# + 1] &]


PROG

(Haskell)
a067611 n = a067611_list !! (n1)
a067611_list = map (`div` 6) $
filter (\x > a010051' (x1) == 0  a010051' (x+1) == 0) [6, 12..]
 Reinhard Zumkeller, Jul 13 2014
(MAGMA) [n: n in [1..100]  not IsPrime(6*n1) or not IsPrime(6*n+1)]; // Vincenzo Librandi, Nov 19 2014
(PARI) for(n=1, 1e2, if(!isprime(6*n+1)  !isprime(6*n1), print1(n", "))) \\ Altug Alkan, Nov 10 2015


CROSSREFS

Cf. A002822, A010051, A037074, A046953, A046954, A060461, A070043, A070799, A121763, A121765, A136017, A136050.
Sequence in context: A180638 A213320 A024887 * A190485 A105803 A202268
Adjacent sequences: A067608 A067609 A067610 * A067612 A067613 A067614


KEYWORD

nonn


AUTHOR

Jon Perry, Feb 01 2002


EXTENSIONS

Edited by Robert G. Wilson v, Feb 05 2002
Edited by Dean Hickerson, May 07 2002


STATUS

approved



