|
Search: id:A114430
|
|
|
| A114430 |
|
Primes of the form 1 + product of the first n 3-almost primes A014612. |
|
+0
1
|
|
| 97, 32920473601, 1448500838401, 65182537728001, 1491301685600774317670400000001
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
3-almost prime analogue of primorial primes A005234 (primes p such that 1 + product of primes up to p is prime) as indexed by A014545 (n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime). In that sense, this sequence is indexed by (2, 8, 9, 10, 19, ...).
|
|
FORMULA
|
{a(n)} = {1 + Prod[from i = 1 to n] A014612(i)} INTERSECTION {A000040}.
|
|
EXAMPLE
|
a(1) = 97 = 96 + 1 = 1 + (8 * 12) = 1 + A014612(1)*A014612(2) = 1 more than the product of the first 2 of the 3-almost primes, and is prime.
a(2) = 32920473601 = 1 + (8 * 12 * 18 * 20 * 27 * 28 * 30 * 42) = 1 more than the product of the first 8 of the 3-almost primes, and is prime.
a(3) = 1 more than the product of the first 9 of the 3-almost primes, and is prime.
a(4) = 1 more than the product of the first 10 of the 3-almost primes, and is prime.
a(5) = 1 more than the product of the first 19 of the 3-almost primes, and is prime.
|
|
CROSSREFS
|
Cf. A000040, A001358, A014612, A002110, A005234, A014545, A112141.
Adjacent sequences: A114427 A114428 A114429 this_sequence A114431 A114432 A114433
Sequence in context: A069419 A057011 A122128 this_sequence A033418 A120310 A129887
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 13 2006
|
|
|
Search completed in 0.002 seconds
|
