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A006279 Denominators of convergents to Cahen's constant: a(n+2) = a(n)^2*a(n+1) + a(n).

%I A006279 M0914 #45 Jul 08 2025 16:45:34
%S A006279 1,1,2,3,14,129,25298,420984147,269425140741515486,
%T A006279 47749585090209528873482531562977121,
%U A006279 3466137915373323052799848584927709551269254572949111609037058632767202
%N A006279 Denominators of convergents to Cahen's constant: a(n+2) = a(n)^2*a(n+1) + a(n).
%C A006279 Shifted square roots of partial quotients in continued fraction expansion of Cahen's constant: a(n) = sqrt(A006280(n+2)). - _Jonathan Sondow_, Aug 20 2014
%D A006279 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A006279 Amiram Eldar, <a href="/A006279/b006279.txt">Table of n, a(n) for n = 0..13</a>
%H A006279 J. L. Davison and Jeffrey O. Shallit, <a href="https://doi.org/10.1007/BF01332350">Continued Fractions for Some Alternating Series</a>, Monatshefte für Mathematik, Vol. 111 (1991), pp. 119-126; <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN362162050_0111&amp;DMDID=DMDLOG_0013&amp;LOGID=LOG_0013&amp;PHYSID=PHYS_0126">alternative link</a>.
%p A006279 A006279 := proc(n) option remember; if n <= 1 then 1 else A006279(n-2)^2*A006279(n-1)+A006279(n-2) fi end:
%p A006279 seq(A006279(n), n=0..10);
%t A006279 a[n_] := a[n] = If[n < 2, 1, a[n-2]^2*a[n-1] + a[n-2]];
%t A006279 Table[a[n], {n, 0, 9}] (* _Jean-François Alcover_, Sep 23 2022 *)
%o A006279 (Python)
%o A006279 from itertools import islice
%o A006279 def A006279_gen(): # generator of terms
%o A006279     a, b = 1, 1
%o A006279     yield a
%o A006279     while True:
%o A006279         yield b
%o A006279         a, b = b, a*(a*b+1)
%o A006279 A006279_list = list(islice(A006279_gen(),10)) # _Chai Wah Wu_, Mar 19 2024
%Y A006279 Cf. A118227, A006280, A006281.
%K A006279 nonn,easy,frac
%O A006279 0,3
%A A006279 _N. J. A. Sloane_
%E A006279 Definition clarified by _Jonathan Sondow_, Aug 20 2014