A155739 - OEIS

A155739

Decimal expansion of the Euler-Mascheroni constant divided by 2.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Ovidiu Furdui, Problem 1870, Mathematics Magazine, Vol. 84, No. 2 (2011), p. 151; A double zeta sum, Solution to Problem 1870 by Joel Schlosberg, ibid., Vol. 85, No. 2 (2012), p. 156.

Michael Penn, A very Riemann-Zeta sum, YouTube video, 2025.

H. F. Sandham, Problem 4286, The American Mathematical Monthly, Vol. 55, No. 3 (1948), p. 165; Euler's Constant, Solution to Problem 4286 by M. S. Klamkin, ibid., Vol. 56, No. 7 (1949), p. 485.

FORMULA

Equals A001620/2 = (1 + A147533)/4.

Equals Sum_{k,m>=1} k*(zeta(k+m)-1)/(k+m)^2 (Furdui, 2011). - Amiram Eldar, Jun 09 2022

Equals Integral_{x>=0} (cos(x^2)-cos(x))/x dx (Sandham, 1948). - Amiram Eldar, Apr 08 2026

EXAMPLE

0.288607832450766430303256045041201215521079667969961799402...

MAPLE

evalf(gamma/2) ;

MATHEMATICA

RealDigits[EulerGamma/2 , 10, 100][[1]] (* G. C. Greubel, Aug 31 2018 *)

PROG

(PARI) default(realprecision, 100); Euler/2 \\ G. C. Greubel, Aug 31 2018

(Magma) R:= RealField(100); EulerGamma(R)/2; // G. C. Greubel, Aug 31 2018

CROSSREFS

Cf. A001620, A147533.

Sequence in context: A359699 A131920 A180308 * A197139 A198367 A395321

Adjacent sequences: A155736 A155737 A155738 * A155740 A155741 A155742

KEYWORD

cons,nonn

AUTHOR

R. J. Mathar, Jan 26 2009

STATUS

approved