login
The OEIS is supported by
the many generous donors to the OEIS Foundation
.
Hints
(Greetings from
The On-Line Encyclopedia of Integer Sequences
!)
A114337
Primes which are 1/3 of the cumulative sum of factorials of primes, if 1 is used as the zeroth prime.
1
3, 43, 1723, 13307323
(
list
;
graph
;
refs
;
listen
;
history
;
text
;
internal format
)
OFFSET
1,1
COMMENTS
No more primes. Starting with a(14) = (1! + ... + 43!)/3 the sum always has a factor of 47.
LINKS
Table of n, a(n) for n=1..4.
FORMULA
Defining prime(0)= 1: a(n) = (1/3)*Sum_{i=0..n}
A000142
(
A000040
(i+1)) iff in
A000040
. a(n) = (1/3)*Sum_{i=0..n}prime(i+1)! iff in
A000040
.
EXAMPLE
prime(0)! = 1! = 1; prime(1)! = 2! = 2.
a(1) = (1! + 2! + 3!)/3 = 9/3 = 3.
a(2) = (1! + 2! + 3! + 5!)/3 = 129/3 = 43.
a(3) = (1! + 2! + 3! + 5! + 7!)/3 = 5169/3 = 1723.
a(4) = (1! + 2! + 3! + 5! + 7! + 11!)/3 = 39921969/3 = 13307323.
MATHEMATICA
f[n_] := (1 + Plus @@ ((Prime@ Range@ n)!))/3; Select[f /@ Range@ 43, PrimeQ@# &] (*
Robert G. Wilson v
, Apr 30 2009 *)
CROSSREFS
Cf.
A000040
,
A000142
.
Sequence in context:
A274387
A300988
A136648
*
A317343
A307248
A009720
Adjacent sequences:
A114334
A114335
A114336
*
A114338
A114339
A114340
KEYWORD
fini
,
full
,
nonn
AUTHOR
Jonathan Vos Post
, Feb 07 2006
STATUS
approved
Lookup
|
Welcome
|
Wiki
|
Register
|
Music
|
Plot 2
|
Demos
|
Index
|
Browse
|
More
|
WebCam
Contribute new seq. or comment
|
Format
|
Style Sheet
|
Transforms
|
Superseeker
|
Recents
The OEIS Community
| Maintained by
The OEIS Foundation Inc.
License Agreements, Terms of Use, Privacy Policy.
.
Last modified April 23 07:42 EDT 2024. Contains 371905 sequences. (Running on oeis4.)