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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 Adjacent sequences:  A007564 A007565 A007566 * A007568 A007569 A007570 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 August 1 11:49 EDT 2021. Contains 346385 sequences. (Running on oeis4.)