|
Search: id:A126263
|
|
|
| A126263 |
|
List of primes generated by factoring successive integers in Sylvester's sequence (A000058). |
|
+0
1
|
|
| 2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 9119521, 6212157481, 5295435634831, 31412519357481261, 77366930214021991992277, 181, 1987, 112374829138729, 114152531605972711
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
The list is infinite and no term repeats since Sylvester's sequence is an infinite coprime sequence.
|
|
REFERENCES
|
F. Saidak, A New Proof of Euclid's Theorem, American Mathematical Monthly, December 2006
|
|
LINKS
|
William Stein, Table of n, a(n) for n = 1..27
Filip Saidak, Proof of Euclid's Theorem.
|
|
MAPLE
|
a(0):=2; for n from 0 to 8 do a(n+1):=a(n)^2-a(n)+1; ifactor(%); od;
|
|
PROGRAM
|
(sage program from William Stein, Aug 26 2009)
v=[2]
for n in range(12):
... v.append(v[-1]^2-v[-1]+1)
... print prime_divisors(v[-1])
[2, 3, 7, 43, 13, 139, 3263443, 547, 607, 1033, 31051, 29881, 67003, 9119521, 6212157481, 5295435634831, 31401519357481261, 77366930214021991992277]
|
|
CROSSREFS
|
Cf. A000058.
Sequence in context: A119662 A163157 A000945 this_sequence A030087 A106864 A085682
Adjacent sequences: A126260 A126261 A126262 this_sequence A126264 A126265 A126266
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Howard L. Warth (hlw6c2(AT)umr.edu), Dec 22 2006
|
|
EXTENSIONS
|
Offset corrected by N. J. A. Sloane, Aug 20 2009
a(23) - a(27) from William Stein (wstein(AT)gmail.com), Aug 20 2009, Aug 21 2009
|
|
|
Search completed in 0.002 seconds
|
