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A256108 Positions of nonzero digits in binary expansion of Pi.

%I A256108 #17 Aug 04 2024 20:49:45
%S A256108 -1,0,3,6,11,12,13,14,15,16,18,19,21,23,25,29,33,38,40,41,43,47,48,53,
%T A256108 57,58,60,63,64,68,71,72,76,77,80,81,85,87,91,93,94,95,103,104,106,
%U A256108 107,108,114,115,116,119,120,122,126,129,131,134,141,144,147,148,149,155,159
%N A256108 Positions of nonzero digits in binary expansion of Pi.
%C A256108 Nonzero entries in A004601 (re-indexed to start at -1 and ascend).
%C A256108 The binary positions (exponents) are negated for convenience (as is standard practice). By the results of the PiHex project, the number 1,000,000,000,000,060 (for example) eventually appears in this sequence. Submitted on 3/14/15, (decimal) Pi Day.
%H A256108 Paolo Xausa, <a href="/A256108/b256108.txt">Table of n, a(n) for n = 1..10000</a>
%H A256108 Steve Pagliarulo, <a href="https://web.archive.org/web/20160324234131/http://members.shaw.ca/francislyster/pi/pistats/pibase2.pdf">Stu's pi page: base 2</a>
%H A256108 Colin Percival, <a href="https://web.archive.org/web/20150827020352/http://oldweb.cecm.sfu.ca/projects/pihex/">PiHex Home Page</a>
%H A256108 Wikipedia, <a href="http://en.wikipedia.org/wiki/PiHex">PiHex</a>
%F A256108 Pi = Sum_{n>=0} 2^(-a(n)).
%F A256108 This sequence A256108 = { i | A004601(1-i) = 1 }. - _M. F. Hasler_, Jul 27 2024
%e A256108 The most significant nonzero binary digit of pi occurs in the 2^1 position. Then there is a digit in the 2^0 position, then the 2^(-3) position, etc. Negate the exponents appearing to get this sequence.
%t A256108 PositionIndex[First[RealDigits[Pi, 2, 200]]][1] - 2 (* _Paolo Xausa_, Aug 04 2024 *)
%o A256108 (PARI) A256108_upto(N)={localbitprec(N+20); [i-2|i<-[1..-20+#N=concat(binary(Pi))], N[i]]} \\ _M. F. Hasler_, Jul 27 2024
%Y A256108 Cf. A004601 (Pi in base 2), A051480.
%K A256108 sign,base
%O A256108 1,3
%A A256108 _David S. Metzler_, Mar 14 2015