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

Author

Peter Luschny, Jan 02 2022

Keywords

• nonn

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.

Examples

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

Links

• 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

Crossrefs

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

Programs

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)])

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)