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User: H. Lee Price

H. Lee Price has authored 2 sequences.

A125667 Eta numbers (from the Japanese word for "pariah" or "outcast"). These are the positive odd integers which cannot be used to make a hypotenuse of a primitive Pythagorean triangle (PPT).

1, 3, 7, 9, 11, 15, 19, 21, 23, 27, 31, 33, 35, 39, 43, 45, 47, 49, 51, 55, 57, 59, 63, 67, 69, 71, 75, 77, 79, 81, 83, 87, 91, 93, 95, 99, 103, 105, 107, 111, 115, 117, 119, 121, 123, 127, 129, 131, 133, 135, 139, 141, 143, 147, 151, 153, 155, 159, 161, 163, 165

Offset: 1

H. Lee Price, Jan 29 2007, corrected Feb 03 2007

nonn

Eta numbers are the odd complement of A020882.
Properties: A PPT hypotenuse has form (4k+1), but the converse is not true. Thus Eta numbers fall into two classes: #1 Odd integers which do not have form (4k+1), #2 Odd integers of form (4k+1) which are not members of A020882.
Eta numbers >1 can be the leg of PPT[a,b,c] but not a hypotenuse, while members of A020882 can be both. By Fermat's theorem, class #2 eta numbers are not prime.

			Class #1 a(6) = E because E is nonnegative, odd and not equal to (4k+1).
Class #2 a(4) = E because E is nonnegative, odd and E=(4k+1) but is not a member of A020882.

H. Lee Price and Frank R. Bernhart, Pythagorean Triples and a New Pythagorean Theorem, arXiv:math.HO/0701554, (2007).
Frank Bernhart and H. Lee Price, Heron's Formula, Descartes Circles and Pythagorean Triangles, arXiv:math.MG/0701624, (2007).

Cf. A020882.

Class #1 a(n) = E because E is nonnegative, odd and not equal to (4k+1). Class #2 a(n) = E because E=(4k+1) (not class #1) but is not a member of A020882.

A125680 Blue moon years > 2000 (new definition), listed with multiplicity, i.e., once for each month having two full moons.

Original entry on oeis.org

2001, 2004, 2007, 2009, 2012, 2015, 2018, 2018, 2020, 2023, 2026, 2028, 2031, 2034, 2037, 2037, 2039, 2042, 2045, 2048, 2050, 2053, 2056, 2058, 2061, 2064, 2066, 2067, 2069, 2072, 2075, 2077, 2080, 2083, 2085, 2088, 2091, 2094, 2094, 2096, 2099, 2102

Offset: 1

H. Lee Price, Jan 30 2007

nonn

A blue moon is the second full moon to occur in a single calendar month. The sequence contains the (Gregorian) years during which each succeeding blue moon will occur.

This is a new version of the definition. The original definition is that of the third full moon in a season which has four. All of the definitions depend on the longitude of the observer. Unless specified otherwise, we should assume that we refer to UTC. A special subsequence is that of the years (1999, 2018, 2037, ...) in which there is no full moon in February, which usually implies that there are two in January as well as in March. This happens most often at an interval of 19 years, but sometimes also 8 or 11 years, for example in 1589, 1608, 1627, 1646, 1665, 1676, 1684, 1695, 1714, 1741, 1752, 1760, 1771, 1790, 1798, 1809, 1828, 1847, 1866... - M. F. Hasler, Dec 08 2017

			a(7) = 2018 because at least one blue moon will occur that year.
a(8) = 2018 because after the first blue moon in January, a second blue moon occurs in March of that year.

Philip Hiscock, Folklore of the Blue Moon, MUN Folklore & Language Archive, Memorial University of Newfoundland, St John's, Newfoundland A1B 3X8, Canada.
Donald W. Olson, What's a Blue Moon?, Sky & Telescope (Archives), May 1999, 36.

David Harper, Blue moon calculator.
Phillip Hiscock, Folklore of the Blue Moon, International Planetarium Society, 1993.
Donald W. Olson, Richard T. Fienberg and Roger W. Sinnott, What's a Blue Moon?, Sky & Telescope, (Archives), Jul 2004, 134.
Wikipedia, Blue Moon.
Index entries for sequences related to calendars

Edited by M. F. Hasler, Dec 08 2017

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User: H. Lee Price

A125667 Eta numbers (from the Japanese word for "pariah" or "outcast"). These are the positive odd integers which cannot be used to make a hypotenuse of a primitive Pythagorean triangle (PPT).

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