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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215414 Unix epoch timestamp for start of year, beginning with 1970. 1
0, 31536000, 63072000, 94694400, 126230400, 157766400, 189302400, 220924800, 252460800, 283996800, 315532800, 347155200, 378691200, 410227200, 441763200, 473385600, 504921600, 536457600, 567993600, 599616000, 631152000, 662688000, 694224000, 725846400, 757382400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This is based on a naive multiplication of A033172 with a fixed number of seconds per year, 24*3600 = 86400. It ignores that leap years are not regularly occurring after 4 years (but after 400 years, note the formula that relates a(n+4) to a(n) and also the simple Mma implementation), ignores leap seconds, and any other influences that align the slowing down of the Earth rotation in an astronomical fixed coordinate system measured relative to atomic clocks. In summary, the use of "year" in the definition is not commensurate with years in standard astronomical or earth observational terms. - R. J. Mathar, Aug 21 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Wikipedia, Unix time

Wikipedia, Leap second

Wikipedia, Revised Julian Calendar

Wikipedia, International Earth Rotation and Reference Systems Service

FORMULA

From Alexander R. Povolotsky, Aug 20 2012: (Start)

a(n) = 10800*(2922*n + (-1)^n + (1+i)*(-i)^n + (1-i)*i^n - 2923).

a(n+4) = a(n) + 126230400.

G.f.: 86400*(365*x +365*x^2 +366*x^3 +365*x^4)/((1-x)^2*(1+x+x^2+x^3)). (End)

MATHEMATICA

lst = {}; t = 86400; Do[e = t*(365*(n - 1) + Ceiling[n/4]); If[! Mod[n, 4] == 0, e = e - t]; AppendTo[lst, e], {n, 25}]; lst (* Arkadiusz Wesolowski, Aug 20 2012 *)

CoefficientList[Series[86400*(365*x + 365*x^2 + 366*x^3 + 365*x^4)/((x - 1)^2*(1 +x +x^2 +x^3)), {x, 0, 50}], x] (* G. C. Greubel, Feb 26 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(86400*(365*x +365*x^2 +366*x^3 +365*x^4)/((1-x)^2*(1+x+x^2+x^3))) \\ G. C. Greubel, Feb 26 2017

CROSSREFS

Cf. A193910.

Sequence in context: A209786 A251530 A125574 * A151621 A052097 A252356

Adjacent sequences:  A215411 A215412 A215413 * A215415 A215416 A215417

KEYWORD

easy,nonn,less

AUTHOR

Kyle Stern, Aug 09 2012

EXTENSIONS

a(11)-a(25) from Arkadiusz Wesolowski, Aug 20 2012

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 November 22 03:35 EST 2019. Contains 329386 sequences. (Running on oeis4.)