|
Search: id:A023203
|
|
|
| A023203 |
|
Numbers n such that n and n + 10 are both prime. |
|
+0
16
|
|
| 3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 139, 157, 163, 181, 223, 229, 241, 271, 283, 307, 337, 349, 373, 379, 409, 421, 433, 439, 457, 499, 547, 577, 607, 631, 643, 673, 691, 709, 733, 751, 787, 811, 829, 853, 877, 919, 937, 967, 1009, 1021, 1039, 1051
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
A subset of A002476[n] Primes of form 6n + 1. It appears that this is also a subset of the Cuban primes A007645[n] Primes of form x^2+xy+y^2; or: primes of form x^2+3*y^2; or: primes == 0 or 1 mod 3. The first few Cuban primes that are not in this sequence are {67,109,151,193,199,211,277,313,331,367,397,463,487,523,541,571,601,613,...}. - Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 15 2006
The entries are all of the cuban form, because they cannot be of the form p=3*k+2. If the were, p+10=3*k+12 were divisible by 3 and not prime. qed. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009]
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
MATHEMATICA
|
Do[s=Prime[n]; If[PrimeQ[s+10], Print[Prime[n]]], {n, 1, 1000}]
|
|
CROSSREFS
|
Different from A015916. Cf. A031928, A079033.
Cf. A002476, A007645.
Sequence in context: A007645 A144919 A015916 this_sequence A086135 A023220 A023205
Adjacent sequences: A023200 A023201 A023202 this_sequence A023204 A023205 A023206
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
David W. Wilson (davidwwilson(AT)comcast.net)
|
|
|
Search completed in 0.002 seconds
|
