Sunday Starting Gregorian Symmetry

Dear Calendar People

 

I list the 53-week years  (from 2000  to 2399) that would occur in the ISO week date calendar if weeks were to begin on Sunday (without reference to existing ISO week date).  These years would be symmetrical about any year whose number is divisible by 200 and the mean new year would be exactly the same as for the Gregorian calendar.

In the second column, the list is modified so that the 53-week years are as uniformly spaced as possible, while retaining the same symmetry and mean new year.

Each 53-week year that is six years from both the previous and next such year is shown in bold and even-number years are shown red.

 

2003   2003

2008   2008

2014   2014

2020   2020

2025   2025

2031   2031

2036   2037

2042   2042

2048   2048

2053   2054

2059   2059

2064   2065

2070   2070

2076   2076

2081   2082

2087   2087

2092   2093

2098   2099

2104   2104

2110   2110

2116   2115

2121   2121

2127   2127

2132   2132

2138   2138

2144   2144

2149   2149

2155   2155

2160   2161

2166   2166

2172   2172

2177   2177

2183   2183

2188   2189

2194   2194

2200   2200

2206   2206

2212   2211

2217   2217

2223   2223

2228   2228

2234   2234

2240   2239

2245   2245

2251   2251

2256   2256

2262   2262

2268   2268

2273   2273

2279   2279

2284   2285

2290   2290

2296   2296

2302   2301

2308   2307

2313   2313

2319   2318

2324   2324

2330   2330

2336   2335

2341   2341

2347   2346

2352   2352

2358   2358

2364   2363

2369   2369

2375   2375

2380   2380

2386   2386

2392   2392

2397   2397

 

I notice that the ISO Week, but on Sunday has three long blocks of even-numbered years around the dropped leap years. The middle years of which are 2104, 2200 and 2296 with intervals of 96 or 208 years.

 

Also all the odd-number years belong to one of 13 pairs without a bold year  (one pair 1997 2003 not shown because it spans end of cycle). These pairs occur in intervals of 28 or 40 years.

The years as uniformly spaced as possible have just 7 such pairs (including the one not shown) and they may be either both even or both odd. They occur in intervals of 62 or 45 years.

 

Indeed  for any leap week rule where the leap year are as uniform as possible, these pairs will come in intervals of 62 or 45 years, unless the mean year is small in which case the intervals will be 62 or 79 years.

This can be seen in http://individual.utoronto.ca/kalendis/leap/52-293-sym454-leap-years.htm for the 293-year cycle with year coloured and bolded in the same way for the 1^st 293-year cycle. The pairs are (20, 26), (82, 88), (144, 150), (206, 212), (268,274). The intervals between the pairs is 62 years within a 293-year cycle and 45 years between 293-year cycles.

 

Karl