login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A249141 Decimal expansion of 'sigma', a constant associated with the expected number of random elements to generate a finite abelian group. 1
2, 1, 1, 8, 4, 5, 6, 5, 6, 3, 4, 7, 0, 1, 6, 3, 5, 3, 2, 3, 8, 2, 5, 2, 7, 7, 6, 9, 1, 0, 2, 3, 6, 4, 7, 6, 4, 2, 8, 8, 5, 9, 0, 7, 8, 5, 6, 1, 8, 5, 1, 7, 9, 1, 5, 4, 1, 4, 2, 6, 3, 8, 5, 2, 9, 0, 9, 8, 3, 4, 1, 1, 2, 3, 6, 5, 3, 4, 6, 3, 4, 5, 7, 7, 5, 5, 7, 0, 8, 2, 5, 9, 7, 8, 1, 8, 7, 6, 7, 9, 3, 9 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.1 Abelian group enumeration constants, p. 273.

LINKS

Table of n, a(n) for n=1..102.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 33.

Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]

Carl Pomerance, The expected number of random elements to generate a finite abelian group, Periodica Mathematica Hungarica 43 (2001), 191-198.

FORMULA

sigma = 1+sum_{j >= 2} (1-prod_{k >= j} zeta(k)^(-1)).

EXAMPLE

2.11845656347016353238252776910236476428859...

MATHEMATICA

digits = 102; jmax = 400; P[j_] := 1/Product[N[Zeta[k], digits+100], {k, j, jmax}]; sigma = 1+Sum[1 - P[j], {j, 2, jmax}]; RealDigits[sigma, 10, digits] // First

PROG

(PARI) default(realprecision, 120); 1 + suminf(j=2, 1 - prodinf(k=j, 1/zeta(k))) \\ Michel Marcus, Oct 22 2014

CROSSREFS

Cf. A021002, A033150, A084892, A084893.

Sequence in context: A053373 A297733 A255812 * A102875 A157785 A021476

Adjacent sequences:  A249138 A249139 A249140 * A249142 A249143 A249144

KEYWORD

nonn,cons,changed

AUTHOR

Jean-Fran├žois Alcover, Oct 22 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)