A099019 Odd composite numbers n such that n-2 and n+2 are also composite.

93, 117, 119, 121, 123, 143, 145, 185, 187, 203, 205, 207, 215, 217, 219, 245, 247, 287, 289, 297, 299, 301, 303, 321, 323, 325, 327, 341, 343, 363, 393, 405, 413, 415, 425, 427, 453, 471, 473, 475, 483, 495, 513, 515, 517, 527, 529, 531, 533, 535, 537, 551

Offset: 1

Author

Rick L. Shepherd, Nov 13 2004

Keywords

• nonn

Comments

No term is the difference of two primes. - Juri-Stepan Gerasimov, Oct 10 2009

Goldbach's conjecture states that all even numbers > 2 can be expressed as the sum of two primes. If true, then this sequence contains all composites which cannot be expressed as the sum or difference of two primes. - Bob Selcoe, Mar 10 2015

Examples

			93 is the first term because 91=7*13, 93=3*31 and 95=5*19 are all composite and there is no smaller odd composite with both odd neighbors composite.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Wikipedia, Goldbach's conjecture

Crossrefs

Subsequence of A007921.

Programs

Mathematica

Select[Range@1200, OddQ@# && AllTrue[{# - 2, #, # + 2}, CompositeQ] &] (* Michael De Vlieger, Mar 10 2015, Version 10 *)

PARI

forstep(n=9,1000,2,if(!isprime(n)&&!isprime(n-2)&&!isprime(n+2),print1(n,",")))