A350471 The number of days elapsed since the Gregorian (proleptic) date Sunday, December 31, 1 BC on 1/1/n, where 1/1/n is the Gregorian date in the format month/day/year, the New Year's Day of the year n.

1, 366, 731, 1096, 1462, 1827, 2192, 2557, 2923, 3288, 3653, 4018, 4384, 4749, 5114, 5479, 5845, 6210, 6575, 6940, 7306, 7671, 8036, 8401, 8767, 9132, 9497, 9862, 10228, 10593, 10958, 11323, 11689, 12054, 12419, 12784, 13150, 13515, 13880, 14245, 14611, 14976, 15341, 15706

Offset

1,2

Comments

The number of days elapsed since the Gregorian date Sunday, December 31, 1 BC is also called the 'absolute date'. Note that there was no year 0. Thus this sequence shows the absolute date of the New Year's Day of the year n.

Links

Table of n, a(n) for n=1..44.

Peter Luschny, Table of n, a(n) for n = 1..3000

Peter Luschny, Calendars, Conversions of Dates, Change of Calendars, GitHub 2022.

John Walker, Calendar Converter.

Wikipedia, Gregorian calendar.

Index entries for sequences related to calendars

Formula

From Robert B Fowler, Aug 20 2024: (Start)

a(n) = 1 + 365*m + floor(m/4) - floor(m/100) + floor(m/400), where m = n-1.

a(n+400*k) = a(n) + 146097*k. (End)

Example

Gregorian date 1/1/2022 = Julian date 12/19/2021 = Hebrew date 10/28/5782 = Islamic date 5/27/1443 = absolute date 738156.

Prog

(Python)
def A350471(n):
    m = n - 1
    return 1 + 365 * m + m // 4 - m // 100 + m // 400
print([A350471(n) for n in range(1, 45)])

Crossrefs

Cf. A350458 (Hebrew Calendar), A350539 (Islamic Calendar).

Sequence in context: A259077 A219960 A033174 * A249704 A260281 A325847

Adjacent sequences: A350468 A350469 A350470 * A350472 A350473 A350474

Keyword

nonn

Author

Peter Luschny, Jan 02 2022

Status

approved