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A165465 Positions of zeros in A165464. Fixed points of A166041/A166042. 5
0, 1, 7, 8, 15, 16, 22, 23, 24, 25, 1702855, 1702856, 1702857, 1702872, 1702873, 2220150, 3327583, 3329174, 3329270, 3329271, 3329279 (list; graph; refs; listen; history; text; internal format)



Consider two immortal sage kings traveling on the infinite chessboard, visiting every square at the leisurely pace of one square per day. Both start their journey at the beginning of the year from the upper left-hand corner square at the day zero (being sages, they can comfortably stay in the same square without bloodshed). One decides to follow the Hilbert I type walk on his never-ending journey, while the other follows the Hilbert II type walk. (These are both illustrated in the entry A166041.) This sequence gives the days when they will meet, when they both come to the same square on the same day.

Both walk first one square towards east, where they meet at Day 1. Then one turns south, while the other one proceeds to the east. However, just six days later, on Day 7, they meet again, at the square (2,1), two squares south and one square east of the starting corner. They also meet the next day (Day 8), as well as another week later (Day 15), and before January is over, they meet still five more times, on Days 16, 22, 23, 24 and 25. However, it takes 4662 years and about three months before they meet again, on three successive days (Days 1702855, 1702856 and 1702857). - Antti Karttunen, Oct 13 2009


A. Karttunen, Table of n, a(n) for n = 0..20


Cf. A165467, A165480, A163901.

Subset of A165480. - Antti Karttunen, Oct 13 2009

Sequence in context: A101517 A015893 A271953 * A047521 A231390 A231458

Adjacent sequences:  A165462 A165463 A165464 * A165466 A165467 A165468




Antti Karttunen, Oct 06 2009



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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.