A215414 Timestamp for start of year, beginning with 1970, similar to Unix.

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

Offset

1,2

Comments

This is based on a naive multiplication of A033172 with a fixed number of seconds per calendar day, 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

From a(132), which represents the start of calendar year 2101, the values are not Unix epoch timestamps, because 2100 is not a leap year. - Ruud H.G. van Tol, Apr 08 2026

Links

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

Ruud H.G. van Tol, Perl code that prints Unix timestamps.

Wikipedia, Unix time.

Wikipedia, Leap second.

Wikipedia, Revised Julian calendar.

Wikipedia, International Earth Rotation and Reference Systems Service.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

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), where i is the imaginary unit.

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, 30}], x] (* G. C. Greubel, Feb 26 2017 *)

Prog

(PARI) my(x='x+O('x^30)); 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
(PARI) a(n)= 24*60*60*(365*(n-1) + n\4); \\ Ruud H.G. van Tol, Apr 10 2026

Crossrefs

Cf. A033172, 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

Edited by Ruud H.G. van Tol, Apr 09 2026

Status

approved