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

Author

David S. Metzler, Mar 14 2015

Keywords

• sign
• base

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.

Examples

			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.
		

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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

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