A003077 -id:A003077 - cp's OEIS frontend

A224365 a(n) = A063674(n+1) - A063674(n).

10, 3, 3, 3, 157, 22, 22, 22, 22, 22, 22, 22, 22, 51808, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355, 355

Offset: 1

Paul Curtz, Apr 09 2013

The repeated terms (3, 22, 355, 5419351, ... from A063674) are the numerators of fractions (3/1, 22/7, 355/113, 5419351/1725033, ...) leading to Pi.
Zu Chongzhi (5th century) discovered 22/7 and 355/113. Adriaan Anthonisz Metius rediscovered 355/113 in 1585.
First differences of A063673 give the denominators: 3, 1, 1, 1, 50, 7, 7, 7, 7, 7, 7, 7, 7, 16489, 113, 113, ... .
Hence 10/3, 157/50, 51808/16489, ... .

Vincenzo Librandi, Table of n, a(n) for n = 1..168

Cf. A063673, A063674.

Cf. A046947, A072398, A002485. A132049, A003077, A068028, A068079.

A224365 = Reap[ For[ delta0 = 1; d = 1, d < 10^5, d++, delta = Abs[Pi - Round[Pi*d]/d]; If[ delta < delta0, Sow[ Round[Pi*d]]; delta0 = delta]]][[2, 1]] // Differences (* Jean-François Alcover, Apr 10 2013 *)

a(n) = A063674(n+1) - A063674(n).

A226042 Decimal expansion of Pi-333/106.

Original entry on oeis.org

0, 0, 0, 0, 8, 3, 2, 1, 9, 6, 2, 7, 5, 2, 9, 0, 8, 7, 5, 1, 9, 2, 4, 7, 1, 5, 6, 8, 6, 4, 4, 0, 8, 5, 4, 4, 5, 7, 4, 5, 2, 7, 8, 8, 9, 9, 4, 1, 1, 4, 3, 5, 5, 6, 8, 2, 4, 0, 0, 1, 1, 9, 6, 0, 8, 1, 4, 0, 1, 3, 1, 1, 9, 4, 6, 5, 8, 6, 3, 5, 7, 1, 1, 8, 6, 0, 0, 8, 6, 3, 0, 7, 7, 9, 6, 6, 1, 2, 4, 5

Offset: 0

Jean-François Alcover, May 24 2013

			0.000083219627529087519247156864408544574527889941143556824001196081401311946...

Cf. A003077, A002485, A002486.

Join[{0, 0, 0, 0}, RealDigits[Pi-333/106, 10, 96][[1]]] (* Jean-François Alcover, May 24 2013 *)

Pi - 333/106 \\ Charles R Greathouse IV, Oct 01 2022

Pi-333/106 = 1/530*integral_{x=0..1} x^5*(1-x)^6*(197+462*x^2)/(1+x^2).

A159878 The digits of Pi whose spellings in English contain no i's.

Original entry on oeis.org

3, 1, 4, 1, 2, 3, 7, 3, 2, 3, 4, 2, 4, 3, 3, 3, 2, 7, 0, 2, 4, 1, 7, 1, 3, 3, 7, 1, 0, 2, 0, 7, 4, 4, 4, 2, 3, 0, 7, 1, 4, 0, 2, 2, 0, 2, 0, 3, 4, 2, 3, 4, 2, 1, 1, 7, 0, 7, 2, 1, 4, 0, 1, 3, 2, 2, 3, 0, 4, 7, 0, 3, 4, 4, 0, 0, 2, 2, 3, 1, 7, 2, 3, 4, 0, 1, 2, 4, 1, 1, 1, 7, 4, 0, 2, 4, 1, 0, 2, 7, 0, 1, 3, 2, 1

Offset: 1

Cino Hilliard, Apr 25 2009

Blind Pi: The series of digits of Pi A000796 after removal of any 5, 6, 8 or 9 (see A095763, A089589).
The difference of the value of this constant to Pi is 0.000355..., compared to a difference of 0.0012... = A003077 for 22/7.
The only other alpha language that has no numbers 0 to 9 with an i is Albanian.
It is natural to ask "is the constant defined in this way irrational, transcendental?"

			Pi = 3.1415... . The digit 5 or five contains an i in the spelling. So 5 is not in the sequence.

Flatten[ RealDigits[Pi, 10, 174][[1]] /. {5 -> {}, 6 -> {}, 8 -> {}, 9 -> {}}] (* Robert G. Wilson v, May 27 2009 *)

blindpi(n) =
{
default(realprecision,1000);
local(pi,x);
pi=Vec(Str(Pi*10^99));
default(realprecision,28);
for(x=1,n,
if(pi[x]=="0"||pi[x]=="1"||pi[x]=="2"||pi[x]=="3"||pi[x]=="4"||pi[x]=="7",
print1(pi[x]",");
);
);
}

Edited by R. J. Mathar, Apr 28 2009

A226043 Decimal expansion of 355/113-Pi.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 2, 6, 6, 7, 6, 4, 1, 8, 9, 0, 6, 2, 4, 2, 2, 3, 1, 2, 3, 6, 8, 9, 3, 2, 8, 8, 6, 4, 9, 6, 3, 3, 3, 8, 0, 4, 0, 5, 1, 9, 5, 2, 3, 2, 7, 8, 0, 7, 3, 4, 3, 6, 3, 9, 4, 7, 8, 4, 8, 8, 6, 4, 3, 7, 7, 0, 7, 0, 4, 9, 4, 1, 4, 4, 3, 8, 4, 9, 8, 4, 1, 2, 8, 0, 8, 5, 2, 5, 7, 3, 1, 9, 7, 5

Offset: 0

Jean-François Alcover, May 24 2013

			0.000000266764189062422312368932886496333804051952327807343639478488643770704...

Cf. A003077, A002485, A002486, A226042.

Join[{0, 0, 0, 0, 0, 0}, RealDigits[355/113 - Pi, 10, 94][[1]]]

355/113-Pi \\ Charles R Greathouse IV, Oct 01 2022

355/113-Pi = 1/3164*integral_{x=0..1} x^8*(1-x)^8*(25+816*x^2)/(1+x^2).

cp's OEIS Frontend

A224365 a(n) = A063674(n+1) - A063674(n).

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A226042 Decimal expansion of Pi-333/106.

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PARI

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A159878 The digits of Pi whose spellings in English contain no i's.

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A226043 Decimal expansion of 355/113-Pi.

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Mathematica

PARI

Formula