|
Search: id:A141399
|
|
|
| A141399 |
|
A positive integer n is included if all the distinct primes that divide n and n+1 together are members of a set of consecutive primes. In other words, n is included if and only if n*(n+1) is contained in sequence A073491. |
|
+0
1
|
|
| 1, 2, 3, 5, 8, 9, 14, 15, 20, 24, 35, 80, 125, 224, 384, 440, 539, 714, 1715, 2079, 2400, 3024, 4374, 9800, 12375, 123200, 194480, 633555
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The smallest prime in the set of consecutive primes is always 2, since n*(n+1) is even.
No more terms less than 10^6. [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008]
|
|
EXAMPLE
|
20 is factored as 2^2 *5^1. 21 is factored as 3^1 *7^1. Since the distinct primes that divide 20 and 21 (which are 2,3,5,7) form a set of consecutive primes, then 20 is in the sequence.
|
|
MAPLE
|
with(numtheory): a:=proc(n) local F, m: F:=`union`(factorset(n), factorset(n+1)): m:=nops(F): if ithprime(m)=F[m] then n else end if end proc: seq(a(n), n=1..1000000); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008]
|
|
CROSSREFS
|
Cf. A073491.
Sequence in context: A058237 A009388 A125871 this_sequence A104737 A120057 A099422
Adjacent sequences: A141396 A141397 A141398 this_sequence A141400 A141401 A141402
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Aug 03 2008
|
|
EXTENSIONS
|
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 12 2008
|
|
|
Search completed in 0.002 seconds
|
