

A099019


Odd composite numbers n such that n2 and n+2 are also composite.


3



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
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OFFSET

1,1


COMMENTS

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



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(n2)&&!isprime(n+2), print1(n, ", ")))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



