A094964 -id:A094964 - cp's OEIS frontend

A191359 Continued fraction using the decimal digits of Pi.

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

Offset: 0

Fabrice Auzanneau, Jun 04 2011

			0.2611882.. = 1/3.82865....

Cf. A000796, A094964.

1/(3+1/(1+1/(4+1/(1+1/(5+1/(9+1/(2+1/(6+1/(5+1/(3+1/(5+1/(8+1/(9+1/(7+1/(9+1/(3+1/(2+1/...))))))))))))))))). [corrected by John M. Campbell, Aug 25 2011]

Equals 1/A094964. - R. J. Mathar, Jun 04 2011

A308226 A continued fraction transformation of Euler-Mascheroni constant.

Original entry on oeis.org

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

Offset: 0

Paolo P. Lava, May 16 2019

This number has the continued fraction which is the decimal expansion of Euler-Mascheroni constant.

			Equals 0.1945474448030236589478037026913009...

Cf. A001620, A094964, A094965.

with(numtheory): P:=proc(q) local a,b,n: a:=evalf(gamma,q): b:=[]:
while a>0 do b:=[op(b),trunc(a)]: a:=evalf(10*(a-trunc(a)),q): od:
a:=b[nops(b)]: for n from nops(b)-1 by -1 to 1 do a:=1/a+b[n]:
od: print(evalf(a,q)); end: P(200):

A332715 Decimal expansion of a continued fraction based on Pi truncated to n places.

Original entry on oeis.org

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

Offset: 1

Eder Vanzei, Feb 20 2020

After a few terms 3.14115... appears in the constant, which is almost Pi.

			3 + 1/(31 + 1/(314 + 1/(3141...)))
= 3.032254750902178079875651108781183141152724389680301643979636739...

Cf. A000796, A011545, A094964.

A011545(1) + 1/(A011545(2) + 1/(A011545(3) + 1/...)).

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A191359 Continued fraction using the decimal digits of Pi.

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A308226 A continued fraction transformation of Euler-Mascheroni constant.

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A332715 Decimal expansion of a continued fraction based on Pi truncated to n places.

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