A073422 -id:A073422 - cp's OEIS frontend

A001467 Denominators of an expansion for Pi.

1, 1, 1, 7, -791, -3748629, 151648960887729, -1323497544567561138595307148089, 41444465282455711991644958522615049159671653083333293470875123

Offset: 0

N. J. A. Sloane

			a(4) = -791 since Pi - (1/1) - (1/1) - (1/1) - (1/7) = -0.001264489... is closer to 1/(-791) = -0.001264222... than to 1/(-790) = -0.0012658228...

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64.
H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.
J. W. Wrench, Jr., Letter to N. J. A. Sloane, Mar 27 1974
Index entries for sequences related to the number Pi

Cf. A001466, A014013, A073422.

x=Pi; for(k=0,8,if(x<1,d=round(1/x),d=1); x=x-1/d; print(d,", ")) \\ Jaume Oliver Lafont, Feb 21 2009

Numerators are 1.

Edited by Henry Bottomley, Jul 30 2002

A243369 Denominators of Egyptian fraction expansion of e, without repetition.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 2355, 17497263, 1860801514823609, 3584505381349378370871887741627, 85751894581999497691951513557530024967086681471033652102477414

Offset: 1

Arlu Genesis A. Padilla, Jun 04 2014

nonn

Slightly different version of A073422, disregarding the repetition of values.
Similar process to A243020 (Denominators of Egyptian fraction expansion of Pi, without repetition).
The integer terms a(1), a(2), ... approximate Euler's constant A001113 = 1/a(1) + 1/a(2) + 1/a(3)+... by a(1)=1 and then selecting a(n) as the smallest positive number not yet in {a(1),...,a(n-1)} such that the remainder A001113 -1/a(1) -1/a(2) ... -1/a(n) remains positive. - R. J. Mathar, Jul 03 2017

			e = 1 + 1/2 + 1/3 + ... + 1/8 + 1/2355 + ...

Arlu Genesis A. Padilla, Table of n, a(n) for n = 1..17

Cf. A073422.

Digits := 1000:
a243369set := {1} ;
for loop from 1 to 13 do
    erest := evalf(exp(1))-add(1/p,p=a243369set) ;
    eivn := ceil(1/erest) ;
    while eivn in a243369set do
        eivn := eivn+1 ;
    end do:
    a243369set := a243369set union {eivn} ;
    print(eivn) ;
end do: # R. J. Mathar, Jul 03 2017

cp's OEIS Frontend

A001467 Denominators of an expansion for Pi.

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