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%I A007541 M4351 #46 Nov 28 2021 16:42:48
%S A007541 1,7,15,292,436,20776,78629,179136,528210,12996958,878783625,
%T A007541 5408240597,5916686112,9448623833,9787547328,52662113289
%N A007541 Incrementally largest terms in the continued fraction for Pi-2 (cf. A001203).
%C A007541 No larger term in the first 10,672,905,501 terms of the c.f. - _Eric W. Weisstein_, Jul 18 2013
%D A007541 R. W. Gosper, Jr., Table of the simple continued fraction for pi and the derived decimal approximation, Math. Comp., 31 (1977), 1044.
%D A007541 R. W. Gosper, personal communication.
%D A007541 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007541 See A001203 for many additional references and links.
%H A007541 H. Havermann, <a href="http://chesswanks.com/pxp/cfpi.html">Simple Continued Fraction for Pi</a> [a 483 MB file containing 180 million terms]
%H A007541 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi.html">Pi</a>
%H A007541 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>
%H A007541 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a>
%t A007541 upto=10^7;a={};r=0;f=ContinuedFraction[Pi-2,upto];Do[If[f[[i]]>r,AppendTo[a,r=f[[i]]]],{i, upto}];a (* _Paolo Xausa_, Nov 28 2021 *)
%o A007541 (PARI) allocatemem(4096*10^6);
%o A007541 default(realprecision, 50000);
%o A007541 v = contfrac(Pi-2);
%o A007541 m = 0;
%o A007541 for (i=1, #v, if (v[i] > m, m = v[i]; print1(m, ", "))); \\ _Michel Marcus_, Aug 05 2017; to get 7 terms
%Y A007541 Cf. A001203, A000796, A033090.
%Y A007541 Apart from initial term, same as A033089.
%K A007541 nonn
%O A007541 1,2
%A A007541 _N. J. A. Sloane_
%E A007541 Corrected (missing a(9) added) by _Eric W. Weisstein_, Dec 08 2010
%E A007541 a(12) from _Eric W. Weisstein_, Dec 08 2010
%E A007541 a(13) from _Eric W. Weisstein_, Sep 16 2011
%E A007541 a(14) from _Eric W. Weisstein_, Sep 17 2011
%E A007541 a(15) from _Eric W. Weisstein_, Jul 18 2013
%E A007541 a(6) corrected by _Bobby Jacobs_, Aug 05 2017
%E A007541 a(16) = A033089(16) from _Jeppe Stig Nielsen_, Nov 28 2021

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