# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a079429 Showing 1-1 of 1 %I A079429 #13 Sep 08 2022 08:45:08 %S A079429 2,3,5,7,11,19,51,307,8499,2105651,17181974835,36028814200938803, %T A079429 618970019678718951650500915, %U A079429 22300745198530623760505737951367313156481331,13803492693581127574869511746854796103432841704846511061692361604079923 %N A079429 a(0) = 2, a(1) = 3, a(2) = 5; a(n) = a(n-1) + [a(n-1)-a(n-2)] * [a(n-2)-a(n-3)]. %H A079429 Robert Israel, Table of n, a(n) for n = 0..19 %F A079429 Conjecture: a(n)=A011455(n-1)+5 where defined. - _R. J. Mathar_, Apr 26 2007 %F A079429 Proof of conjecture: if d(n) = log_2(a(n+1)-a(n)), we have d(0)=0, d(1)=1, d(n)=d(n-1)+d(n-2), so d(n) = Fibonacci(n). - _Robert Israel_, Oct 25 2017 %e A079429 a(3) = 7, since a(3) = a(2) + [(a(2)-a(1)) * (a(1)-a(0))] = 5 + ((5-3)*(3-2)) %p A079429 f:= proc(n) option remember; procname(n-1)+(procname(n-1)-procname(n-2))*(procname(n-2)-procname(n-3)) end proc: %p A079429 f(0):= 2: f(1):= 3: f(2):= 5: %p A079429 map(f, [$0..20]); # _Robert Israel_, Oct 25 2017 %t A079429 a[0] = 2; a[1] = 3; a[2] = 5; a[n_] := a[n] = a[n - 1] + (a[n - 1] - a[n - 2])*(a[n - 2] - a[n - 3]); Table[a[n], {n, 0, 14}] %o A079429 (Magma) I:=[2,3,5]; [n le 3 select I[n] else Self(n-1)+(Self(n-1)-Self(n-2))*(Self(n-2)-Self(n-3)): n in [1..15]]; // _Vincenzo Librandi_, Oct 25 2017 %Y A079429 Cf. A011455. %K A079429 nonn %O A079429 0,1 %A A079429 Ajay Chhabra (ajay(AT)cantab.net), Jan 08 2003 %E A079429 Edited, corrected and extended by _Robert G. Wilson v_, Jan 08 2002 %E A079429 Conjecture corrected by _Robert Israel_, Oct 25 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE