|
Search: id:A104657
|
|
|
| A104657 |
|
Positive integers n such that n^19 + 1 is semiprime (A001358). |
|
+0
3
|
|
| 2, 10, 28, 106, 190, 292, 556, 756, 858, 906, 1012
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
We have the polynomial factorization: n^19 + 1 = (n + 1) * (n^18 - n^17 + n^16 - n^15 + n^14 - n^13 + n^12 - n^11 + n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1). Hence after the initial n=1 prime the binomial can never be prime. It can be semiprime iff n+1 is prime and (n^18 - n^17 + n^16 - n^15 + n^14 - n^13 + n^12 - n^11 + n^10 - n^9 + n^8 - n^7 + n^6 - n^5 + n^4 - n^3 + n^2 - n + 1) is prime.
|
|
FORMULA
|
a(n)^19 + 1 is semiprime (A001358).
|
|
EXAMPLE
|
2^19 + 1 = 524289 = 3 * 174763,
10^19 + 1 = 10000000000000000001 = 11 * 909090909090909091,
1012^19 + 1 =
125438178100868833265294241234853844232270960601988910249
= 1013 *
1238284087866424810121364671617510801898035149081825373.
|
|
CROSSREFS
|
Cf. A000040, A001358, A006313, A103854, A104238, A104335, A105041, A105066, A105078, A105122, A105142, A105237, A104479, A104494.
Sequence in context: A109723 A053594 A006331 this_sequence A000900 A124023 A127921
Adjacent sequences: A104654 A104655 A104656 this_sequence A104658 A104659 A104660
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 21 2005
|
|
|
Search completed in 0.002 seconds
|
