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A097105 Gregorian years containing "blue" Islamic New Year Days. The boundary of a calendrical period is hereby called "blue" w.r.t. a similarly named period in another calendar when the shorter one does not contain the boundaries of the longer one. Gregorian calendar prior to 1582 is proleptic, extrapolated according to the calculator in the links. 0
640, 672, 705, 738, 770, 803, 835, 868, 900, 933, 966, 998, 1031, 1063, 1096, 1129, 1161, 1194, 1226, 1259, 1291, 1324, 1357, 1389, 1422, 1454, 1487, 1520, 1552, 1585, 1617, 1650, 1682, 1715, 1748, 1780, 1813, 1845, 1878, 1911, 1943, 1976, 2008, 2041 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The ratio of Gregorian to Islamic Year is 365.2425/354.36666... = 438291/425240. The interesting approximating continuous fractions are 403/391, 638/619, 1041/1010 and a very long sequence of (1041+403*n)/(1010+391*n), ending with 7489/7266, so the 403/391 pattern will remain for thousands of years.

LINKS

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

John Walker, Calendar Converter

EXAMPLE

1396-1-1 A.H. = 1976-1-3 C.E.

1397-1-1 A.H. = 1976-12-22 C.E. therefore 1976 is listed.

CROSSREFS

Sequence in context: A250587 A293922 A027885 * A233911 A178975 A170774

Adjacent sequences:  A097102 A097103 A097104 * A097106 A097107 A097108

KEYWORD

nonn

AUTHOR

Leonid Broukhis, Sep 15 2004

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)