A222171 - OEIS

A222171

Decimal expansion of Pi^2/24.

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

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OFFSET

0,1

REFERENCES

George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press, 2006, p. 242.

Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 3.45, p. 158 and 199-200.

LINKS

Table of n, a(n) for n=0..99.

Index entries for transcendental numbers

FORMULA

Equals Integral_{x=0..Pi/2} log(sec(x))/tan(x) dx.

Equals Sum_{k >= 1} 1/(2k)^2. - Geoffrey Critzer, Nov 02 2013

Equals (1/10) * Sum_{k>=1} d(k^2)/k^2, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 27 2020

Equals Sum_{n >= 0} 1/((2*n+1)*(6*n+3)). - Peter Bala, Feb 02 2022

Equals Sum_{n>=0} ((-1)^n * (Sum_{k>=n+1} (-1)^k/k)^2) (Furdui, 2013). - Amiram Eldar, Mar 26 2022

EXAMPLE

0.411233516712056609118103791661506297304737475301699609433889557342501867600...

MATHEMATICA

RealDigits[Pi^2/24, 10, 100] // First

PROG

(Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^100*(pi)^2/24))); // Vincenzo Librandi, Sep 25 2015

(PARI) Pi^2/24 \\ Michel Marcus, Dec 10 2020

CROSSREFS

Cf. A000005, A013679, A111003, A072691, A078471.

Sequence in context: A016526 A247341 A030747 * A325529 A264534 A228489

Adjacent sequences: A222168 A222169 A222170 * A222172 A222173 A222174

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, May 13 2013

EXTENSIONS

Leading 0 term removed (to make offset correct) by Rick L. Shepherd, Jan 01 2014

STATUS

approved