cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A366397 Decimal expansion of the number whose continued fraction terms are one larger than those of Pi.

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%I A366397 #11 Dec 12 2023 19:33:39
%S A366397 4,1,2,4,0,6,0,1,0,2,2,8,7,8,6,5,3,9,1,6,7,5,8,5,0,8,3,2,2,5,6,8,1,7,
%T A366397 4,9,7,8,4,2,0,1,8,3,7,2,9,7,3,9,1,3,5,6,7,7,0,7,3,4,3,4,3,5,6,2,3,1,
%U A366397 8,9,4,5,4,1,5,8,9,1,8,0,1,6,8,3,3,3,3,1,5,4,4,2,9,7,0,6,8,1,0,3,0,3,6,0
%N A366397 Decimal expansion of the number whose continued fraction terms are one larger than those of Pi.
%H A366397 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a366/A366397.java">Java program</a> (github)
%e A366397 4.12406010228786539167585... = 4 + 1/(8 + 1/(16 + 1/(2 + 1/(293 + ...)))).
%e A366397 Pi = 3.141592653589793238... = 3 + 1/(7 + 1/(15 + 1/(1 + 1/(292 + ...)))).
%o A366397 (PARI)
%o A366397 N = 25;
%o A366397 cf(v) = my(m=contfracpnqn(v)); m[1, 1]/m[2, 1];
%o A366397 summand(k) = (-1)^k/2^(10*k)*(-2^5/(4*k+1)-1/(4*k+3)+2^8/(10*k+1)-2^6/(10*k+3)-2^2/(10*k+5)-2^2/(10*k+7)+1/(10*k+9));
%o A366397 pi1 = contfrac(1/2^6*sum(k=0,N,summand(k)));
%o A366397 pi2 = contfrac(1/2^6*sum(k=0,N+1,summand(k)));
%o A366397 n = 0; while(pi1[1..n+1] == pi2[1..n+1], n++);
%o A366397 ap1 = cf(apply(x->x+1, pi1[1..n-1]));
%o A366397 ap2 = cf(apply(x->x+1, pi1[1..n]));
%o A366397 n = 0; while(digits(floor(10^(n+1)*ap1)) == digits(floor(10^(n+1)*ap2)), n++);
%o A366397 A366397 = digits(floor(10^n*ap1));
%Y A366397 Cf. A000796, A001203, A059833.
%K A366397 cons,nonn
%O A366397 1,1
%A A366397 _Rok Cestnik_, Oct 08 2023