A132715 - OEIS

A132715

Decimal expansion of 25/Pi.

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

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OFFSET

1,1

COMMENTS

Starting with 0, 0, 7, 9, 5, ... this is also the decimal expansion of 1/(4*Pi). Example: 0.079577471545947667884441881686257181... - Omar E. Pol, Jan 18 2013

LINKS

Table of n, a(n) for n=1..105.

Srinivasa Ramanujan, Question 463, Journal of the Indian Mathematical Society, Vol. 5 (1913), p. 120.

H. F. Sandham, Problem 4585, The American Mathematical Monthly, Vol. 61, No. 4 (1954), p. 263; A Series Involving the Partition Functin, Solution to Problem 4585, by Chih-yi Wang, ibid., Vol. 62, No. 6 (1955), pp. 451-452.

H. F. Sandham, Some infinite series, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 430-436.

Index entries for transcendental numbers.

FORMULA

1/(4*Pi) = Integral_{x>=0} cos(Pi*x/2)/(exp(2*Pi*sqrt(x))-1) dx (Ramanujan, 1913). - Amiram Eldar, Jan 01 2025

From Amiram Eldar, Apr 08 2026: (Start)

1/(4*Pi) = Sum_{k>=1} k*p(k)/cosh(sqrt(2*k-1/4)*Pi), where p(k) = A000041(k) is the number of partitions of k (Sandham, Problem 4585, 1954).

1/(4*Pi) = Sum_{k>=1} (-1)^(k+1)*k/sinh(k*Pi) (Sandham, 1954, p. 430, eq. 1.31). (End)

EXAMPLE

7.9577471545947667884441881686257181...

MATHEMATICA

RealDigits[25/Pi, 10, 120][[1]] (* Harvey P. Dale, Nov 24 2012 *)

PROG

(PARI) 25/Pi \\ Charles R Greathouse IV, Oct 01 2022

(Magma) R:= RealField(100); 25/Pi(R); // Vincenzo Librandi, Jan 01 2025

CROSSREFS

Cf. A000041, A049541, A060294, A089491, A088538, A086201, A132696 to A132699, A132701, A132702.

Sequence in context: A198417 A363687 A215736 * A154910 A389038 A063603

Adjacent sequences: A132712 A132713 A132714 * A132716 A132717 A132718

KEYWORD

cons,easy,nonn,changed

AUTHOR

Omar E. Pol, Aug 31 2007, Dec 30 2008

EXTENSIONS

More digits from R. J. Mathar, Aug 17 2009

STATUS

approved