|
| |
|
|
A109611
|
|
Chen primes: primes p such that p + 2 is either a prime or a semiprime.
|
|
58
|
|
|
|
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101, 107, 109, 113, 127, 131, 137, 139, 149, 157, 167, 179, 181, 191, 197, 199, 211, 227, 233, 239, 251, 257, 263, 269, 281, 293, 307, 311, 317, 337, 347, 353, 359, 379, 389, 401, 409
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
43 is the first prime which is not a member (see A102540).
Contains A001359 = lesser of twin primes.
A063637 is a subsequence. [From Reinhard Zumkeller, Mar 22 2010]
|
|
|
REFERENCES
|
B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, 2005, pp. 5, 14, 18 - 19, 21
|
|
|
LINKS
|
R. J. Mathar, Table of n, a(n) for n = 1..34076
B. Green and T. Tao, Restriction theory of the Selberg sieve, with applications, arXiv:math/0405581 [math.NT]
Eric Weisstein's World of Mathematics, Chen's Theorem
Eric Weisstein's World of Mathematics, Chen Prime
Wikipedia, Chen prime
|
|
|
FORMULA
|
a(n)+2 = A139690(n).
|
|
|
EXAMPLE
|
a(4) = 7 because 7 + 2 = 9 and 9 is a semiprime.
a(5) = 11 because 11 + 2 = 13, a prime.
|
|
|
MAPLE
|
A109611 := proc(n)
option remember;
if n =1 then
2;
else
a := nextprime(procname(n-1)) ;
while true do
if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
return a;
end if;
a := nextprime(a) ;
end do:
end if;
end proc: # R. J. Mathar, Apr 26 2013
|
|
|
MATHEMATICA
|
semiPrimeQ[x_] := TrueQ[Plus @@ Last /@ FactorInteger[ x ] == 2]; Select[Prime[Range[100]], PrimeQ[ # + 2] || semiPrimeQ[ # + 2] &] (* Alonso del Arte, Aug 08 2005 *)
|
|
|
PROG
|
(PARI) isA001358(n)={ if( bigomega(n)==2, return(1), return(0) ); } isA109611(n)={ if( ! isprime(n), return(0), if( isprime(n+2), return(1), return( isA001358(n+2)) ); ); } { n=1; for(i=1, 90000, p=prime(i); if( isA109611(p), print(n, " ", p); n++; ); ); } /* R. J. Mathar, Aug 20 2006*/
|
|
|
CROSSREFS
|
Cf. A001358.
Cf. A112021, A112022, A139689.
Sequence in context: A052042 A086472 A219669 * A181325 A078133 A238242
Adjacent sequences: A109608 A109609 A109610 * A109612 A109613 A109614
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Paul Muljadi, Jul 31 2005
|
|
|
EXTENSIONS
|
Corrected by Alonso del Arte, Aug 08 2005
|
|
|
STATUS
|
approved
|
| |
|
|
