|
Search: id:A105282
|
|
|
| A105282 |
|
Positive integers n such that n^20 + 1 is semiprime (A001358). |
|
+0
2
|
| |
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
We have the polynomial factorization: n^20 + 1 = (n^4 + 1) * (n^16 - n^12 + n^8 - n^4 + 1). Hence after the initial n=1 prime, the binomial can never be prime. It can be semiprime iff n^4+1 is prime and (n^16 - n^12 + n^8 - n^4 + 1) is prime.
|
|
FORMULA
|
a(n)^20 + 1 is semiprime (A001358).
|
|
EXAMPLE
|
2^20 + 1 = 1048577 = 17 * 61681,
4^20 + 1 = 1099511627777 = 257 * 4278255361,
46^20 + 1 = 1799519816997495209117766334283777 = 4477457 * 401906666439788301510827761,
1434^20 + 1 =
1352019721694375552250489804528860551814233886722212960509362177 =
4228599998737 * 319732233386510278346888399489424537759394853595121.
|
|
CROSSREFS
|
Cf. A000040, A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479, A104494, A104657.
Sequence in context: A141142 A007596 A050588 this_sequence A018325 A099804 A019596
Adjacent sequences: A105279 A105280 A105281 this_sequence A105283 A105284 A105285
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost2(AT)yahoo.com), Apr 25 2005
|
|
|
Search completed in 0.002 seconds
|
