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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
Sequence in context: A112196 A021035 A259967 * A093055 A285733 A106335
KEYWORD
sign,easy,nice
AUTHOR
EXTENSIONS
More terms from Christian G. Bower, Oct 15 1999
One additional term from Harvey P. Dale, Oct 19 2012
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)