|
| |
|
|
A144743
|
|
Recurrence sequence a(n)=a(n-1)^2-a(n-1)-1, a(0)=3.
|
|
6
|
|
|
|
3, 5, 19, 341, 115939, 13441735781, 180680260792773944179, 32645356640144805339284259388335434039861, 1065719310162246533488642668727242229836148490441005113524301742665845135502859459
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
a(0)=3 is the smallest integer generating an increasing sequence of the form a(n)=a(n-1)^2-a(n-1)-1.
Conjecture: A130282 and this sequence are disjoint. If this is true, for n >= 1, a(n+1) is the smallest m such that (m^2-1) / (a(n)^2-1) + 1 is a square. - Jianing Song, Mar 19 2022
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = a(n-1)^2-a(n-1)-1, a(0)=3.
a(n) ~ c^(2^n), where c = 2.07259396780115004655284076205241023281287049774423620992171834046728756... . - Vaclav Kotesovec, May 06 2015
|
|
|
MATHEMATICA
|
a = {3}; k = 3; Do[k = k^2 - k - 1; AppendTo[a, k], {n, 1, 10}]; a
|
|
|
PROG
|
(PARI) a(n, s=3)=for(i=1, n, s=s^2-s-1); s \\ M. F. Hasler, Oct 06 2014
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
