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.

A132024 Decimal expansion of Product_{k>=0} (1-1/(2*8^k)).

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%I A132024 #12 May 09 2023 09:59:10
%S A132024 4,6,4,5,6,8,8,8,3,6,8,6,4,7,6,3,9,0,9,8,1,9,5,9,5,6,9,7,4,8,4,7,8,0,
%T A132024 1,0,8,7,0,0,5,8,5,1,5,4,9,5,1,2,3,0,6,5,5,6,6,0,8,5,6,0,5,9,7,0,6,0,
%U A132024 9,9,5,7,6,2,7,4,4,1,5,4,3,8,4,8,7,8,8,8,1,2,5,0,7,6,2,1,9,4,7,0,8,1,7
%N A132024 Decimal expansion of Product_{k>=0} (1-1/(2*8^k)).
%F A132024 Equals lim inf_{n->oo} Product_{k=0..floor(log_8(n))} floor(n/8^k)*8^k/n.
%F A132024 Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^(1/2*(1+floor(log_8(n)))*floor(log_8(n))).
%F A132024 Equals lim inf_{n->oo} A132032(n)/n^(1+floor(log_8(n)))*8^A000217(floor(log_8(n))).
%F A132024 Equals (1/2)*exp(-Sum_{n>0} 8^(-n)*Sum_{k|n} 1/(k*2^k)).
%F A132024 Equals lim inf_{n->oo} A132032(n)/A132032(n+1).
%F A132024 Equals Product_{n>=0} (1 - 1/A013730(n)). - _Amiram Eldar_, May 09 2023
%e A132024 0.46456888368647639098...
%t A132024 RealDigits[QPochhammer[1/2,1/8],10,120][[1]] (* _Harvey P. Dale_, May 23 2011 *)
%o A132024 (PARI) prodinf(k=0, 1 - 1/(2*8^k)) \\ _Amiram Eldar_, May 09 2023
%Y A132024 Cf. A048651, A098844, A067080, A132019, A132026, A132032, A132036, A000217, A013730.
%K A132024 nonn,cons
%O A132024 0,1
%A A132024 _Hieronymus Fischer_, Aug 14 2007
%E A132024 Name corrected by _Amiram Eldar_, May 09 2023