A046953 Numbers k such that 6*k - 1 is composite.

6, 11, 13, 16, 20, 21, 24, 26, 27, 31, 34, 35, 36, 37, 41, 46, 48, 50, 51, 54, 55, 56, 57, 61, 62, 63, 66, 68, 69, 71, 73, 76, 79, 81, 83, 86, 88, 89, 90, 91, 92, 96, 97, 101, 102, 104, 105, 106, 111, 112, 115, 116, 118, 119, 121, 122, 123, 125, 126, 128

Offset: 1

Author

Felice Russo

Keywords

• nonn

Comments

These numbers can be written as 6*x*y + x - y for x > 0, y > 0. - Ron R Spencer, Aug 01 2016

Examples

			a(1)=6 because 6*6 - 1 = 35, which is composite.
		

Links

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

Crossrefs

Cf. A046954, A008588, A016969, subsequence of A067611.

Cf. A024898 (complement).

Programs

GAP

Filtered([1..200], k-> not IsPrime(6*k-1)) # G. C. Greubel, Feb 21 2019

Haskell

a046953 n = a046953_list !! (n-1)
a046953_list = map (`div` 6) $
   filter ((== 0) . a010051' . subtract 1) [6,12..]
-- Reinhard Zumkeller, Jul 13 2014

Magma

[n: n in [1..200] | not IsPrime(6*n-1)]; // G. C. Greubel, Feb 21 2019

Maple

remove(k-> isprime(6*k-1), [$1..130])[]; # Muniru A Asiru, Feb 22 2019

Mathematica

Select[Range[200],!PrimeQ[6#-1]&] (* Vladimir Joseph Stephan Orlovsky, Feb 25 2011 *)

PARI

is(n)=!isprime(6*n-1) \\ Charles R Greathouse IV, Aug 01 2016

Sage

[n for n in (1..200) if not is_prime(6*n-1)] # G. C. Greubel, Feb 21 2019

Formula

a(n) ~ n. - Charles R Greathouse IV, Aug 01 2016