|
Search: id:A107986
|
|
|
| A107986 |
|
Composite numbers of the form p+2 where p is prime. |
|
+0
2
|
|
| 4, 9, 15, 21, 25, 33, 39, 45, 49, 55, 63, 69, 75, 81, 85, 91, 99, 105, 111, 115, 129, 133, 141, 153, 159, 165, 169, 175, 183, 195, 201, 213, 225, 231, 235, 243, 253, 259, 265, 273, 279, 285, 295, 309, 315, 319, 333, 339, 351, 355, 361, 369, 375, 381, 385, 391
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
This sequence is analogous to the sequence formed by the Goldbach-Euler conjecture that every even number greater than 2 is the sum of 2 primes. If p+2 is prime then p and p+2 are twin primes. The number of terms in this sequence is infinite. This follows immediately from the proof that the number of primes p is infinite. Conjecture: The ratio of the number of terms in this sequence to Pi(n) tends to a limit < 1.
|
|
MATHEMATICA
|
f[n_]:=PrimeQ[n+2]; lst={}; Do[p=Prime[n]; If[ !f[p], AppendTo[lst, p+2]], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 22 2009]
|
|
PROGRAM
|
(PARI) sum2pr(n) = \Composite numbers of form p+2. { c=0; cp=0; forprime(x=2, n, cp++; y=x+2; if(isprime(y)==0, c++; print1(y", ") ) ); print(); print(c/cp+.) }
|
|
CROSSREFS
|
Cf. A067774.
Sequence in context: A166131 A122927 A078505 this_sequence A062721 A104243 A099055
Adjacent sequences: A107983 A107984 A107985 this_sequence A107987 A107988 A107989
|
|
KEYWORD
|
easy,nonn,new
|
|
AUTHOR
|
Cino Hilliard (hillcino368(AT)gmail.com), Jun 13 2005
|
|
|
Search completed in 0.002 seconds
|
