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A067611 Numbers of the form 6xy +- x +- y, where x, y are positive integers. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Equivalently, numbers n such that either 6n-1 or 6n+1 is composite (or both are).

Numbers k such that 36k^2-1 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 == (5k-1) mod (6k-1);

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(3k-1) (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*n-1):

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 !! (n-1)

a067611_list = map (`div` 6) $

   filter (\x -> a010051' (x-1) == 0 || a010051' (x+1) == 0) [6, 12..]

-- Reinhard Zumkeller, Jul 13 2014

(MAGMA) [n: n in [1..100] | not IsPrime(6*n-1) or not IsPrime(6*n+1)]; // Vincenzo Librandi, Nov 19 2014

(PARI) for(n=1, 1e2, if(!isprime(6*n+1) || !isprime(6*n-1), 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

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Last modified June 28 04:43 EDT 2017. Contains 288813 sequences.