A153167 Numbers n such that n+2 is not a Chen prime.

2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 88, 89, 90

Offset: 1

Author

Vincenzo Librandi, Dec 20 2008

Keywords

• nonn

Comments

Contains all strictly positive even numbers A005843.

For each odd k>1 we can accumulate the numbers == k^2-2 (mod 2k) in a row, the last entry equal to A073577(k):

7; (k=3)

13, 23; (k=5)

19, 33, 47; (k=7)

25, 43, 61, 79; (k=9)

31, 53, 75, 97, 119; (k=11)

7, 63, 89, 115, 141, 167; (k=13)

43, 73, 103, 133, 163, 193,223; (k=17)

49, 83, 17, 151,185, 219, 253, 287; (k=19)

Each element T of this table has the format T= k^2-2-j*2*k, so T+2 is of the form k*(k-2*j), therefore not prime, and consequently all elements T are in the sequence.

Crossrefs

Cf. A109611, A040976, A073577, A067076.

Extensions

Edited, 41, 59 (see A102540) etc. inserted by R. J. Mathar, Oct 16 2009