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

1,1

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

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Wikipedia, Goldbach's conjecture

Example

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.

Mathematica

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

Prog

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

Crossrefs

Subsequence of A007921.

Sequence in context: A020320 A039550 A167776 * A082131 A249300 A153684

Adjacent sequences: A099016 A099017 A099018 * A099020 A099021 A099022

Keyword

nonn

Author

Rick L. Shepherd, Nov 13 2004

Status

approved