A189824 Decimal expansion of Pogson's ratio 100^(1/5).

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

Offset

1,1

Comments

Ratio appearing in the definition of the astronomical magnitude (brightness) scale.

Named after the English astronomer Norman Robert Pogson (1829-1891). - Amiram Eldar, Apr 24 2021

References

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See p. 232.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Norman Pogson, Magnitudes of Thirty-Six of the Minor Planets for the First Day of Each Month of the Year 1857, Monthly Notices of the Royal Astronomical Society, Vol. 17, No. 1 (1856), pp. 12-15.

Eric Weisstein's World of Mathematics, Pogson's Ratio.

Formula

Equals (5/2)*(1 + Sum_{k>0} (-1)^(k+1)*(3/125)^k*Product_{i=1..k} i^2/(5*i) ) [Knopp]. - Stefano Spezia, Jan 30 2026

Example

2.511886431509580111085032067799...

Mathematica

First[RealDigits[100^(1/5), 10, 200]]

Prog

(PARI) 10^.4 \\ Charles R Greathouse IV, Jan 15 2015
(Magma) 10^(2/5); // G. C. Greubel, Jan 14 2018

Crossrefs

Sequence in context: A024548 A376316 A197737 * A197814 A091772 A275479

Adjacent sequences: A189821 A189822 A189823 * A189825 A189826 A189827

Keyword

nonn,easy,cons

Author

Eric W. Weisstein, Apr 28 2011

Status

approved