A256108 Positions of nonzero digits in binary expansion of Pi.

-1, 0, 3, 6, 11, 12, 13, 14, 15, 16, 18, 19, 21, 23, 25, 29, 33, 38, 40, 41, 43, 47, 48, 53, 57, 58, 60, 63, 64, 68, 71, 72, 76, 77, 80, 81, 85, 87, 91, 93, 94, 95, 103, 104, 106, 107, 108, 114, 115, 116, 119, 120, 122, 126, 129, 131, 134, 141, 144, 147, 148, 149, 155, 159

Offset

1,3

Comments

Nonzero entries in A004601 (re-indexed to start at -1 and ascend).

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.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Steve Pagliarulo, Stu's pi page: base 2

Colin Percival, PiHex Home Page

Wikipedia, PiHex

Formula

Pi = Sum_{n>=0} 2^(-a(n)).

This sequence A256108 = { i | A004601(1-i) = 1 }. - M. F. Hasler, Jul 27 2024

Example

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.

Mathematica

PositionIndex[First[RealDigits[Pi, 2, 200]]][1] - 2 (* Paolo Xausa, Aug 04 2024 *)

Prog

(PARI) A256108_upto(N)={localbitprec(N+20); [i-2|i<-[1..-20+#N=concat(binary(Pi))], N[i]]} \\ M. F. Hasler, Jul 27 2024

Crossrefs

Cf. A004601 (Pi in base 2), A051480.

Sequence in context: A144562 A102889 A183543 * A028744 A028775 A223910

Adjacent sequences: A256105 A256106 A256107 * A256109 A256110 A256111

Keyword

sign,base

Author

David S. Metzler, Mar 14 2015

Status

approved