|
|
A007567
|
|
Knopfmacher expansion of 1/2: a(n+1) = a(n-1)(a(n)+1)-1.
(Formerly M2242)
|
|
0
|
|
|
-3, -2, 2, 5, 11, 59, 659, 38939, 25661459, 999231590939, 25641740502411581459, 25622037156669717708454796390939, 656993627914472375437286314449293585586011019581459, 16833515146119850260546015286782697097805280607642932235667159033564811666316390939
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
REFERENCES
|
A. Knopfmacher, "Rational numbers with predictable Engel product expansions," in G. E. Bergum et al., eds., Applications of Fibonacci Numbers. Vol. 5, pp. 421-427.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ c^(phi^n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio and c = 1.438209999512701281674411567... . - Vaclav Kotesovec, Mar 06 2016
|
|
MATHEMATICA
|
nxt[{a_, b_}]:={b, a(b+1)-1}; Join[{-3, -2}, Transpose[NestList[nxt, {2, 5}, 12]][[1]]] (* Harvey P. Dale, Oct 19 2012 *)
Flatten[{-3, -2, RecurrenceTable[{a[n+1] == a[n-1]*(a[n] + 1) - 1, a[1] == 2, a[2] == 2}, a, {n, 2, 14}]}] (* Vaclav Kotesovec, Mar 06 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|