|
| |
|
|
A126604
|
|
a(1) = 4; a(2) = 3; for n>2, a(n) = a(n-1)^2 + a(n-1) - 1.
|
|
1
| |
|
|
4, 3, 11, 131, 17291, 298995971, 89398590973228811, 7992108067998667938125889533702531, 63873791370569400659097694858350356285036046451665934814399129508491
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| a(n) = -1 + Prod_{k=1..n-1}a(k) for n>1.
Sequence is a variant of A005267 (start values 3 and 2, offset 0). Both sequences have the same recursion formulae and both are infinite coprime sequences; a(n) has digital root 2 for odd n and 5 for even n, n > 2.
a(2) to a(6) are prime, a(1) and a(7) to a(10) are composite, a(2) to a(10) are squarefree.
|
|
|
EXAMPLE
| a(3) = 3^2+3-1 = 11, a(4) = 11^2+11-1 = 131.
|
|
|
MAPLE
| a[1]:=1: a[2]:=3: for n from 3 to 10 do a[n]:=a[n-1]^2+a[n-1]-1 od: seq(a[n], n=1..10); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 09 2007
|
|
|
PROG
| (PARI) 1. {print1(4, ", ", a=3, ", "); for(n=1, 8, print1(a=a^2+a-1, ", "))}
2. {m=10; v=vector(m); print1(v[1]=4, ", "); for(n=2, m, print1(v[n]=-1+prod(k=1, n-1, v[k]), ", "))} - Klaus Brockhaus, Jan 09 2007
|
|
|
CROSSREFS
| Cf. A005267.
Sequence in context: A065337 A072802 A093726 * A191617 A169704 A204291
Adjacent sequences: A126601 A126602 A126603 * A126605 A126606 A126607
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Tomas Xordan (xordan.tom(AT)gmail.com), Jan 06 2007
|
|
|
EXTENSIONS
| Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 09 2007
|
| |
|
|
