Numbers 800,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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800,003

[Math.]  Sequence of numbers 80…032 = 640…0480…09).

800,0032 = 640,004,800,009 = (–6+4–0004+800009)2.

 

800,005

[Math.]  (Sequence of numbers 80…052 = 640…080…025).

800,0052 = 640,008,000,025 = (–6+4+000+800002+5)2.

 

802,010

[Math.]  Two consecutive sums of consecutive square numbers:

2532+2542+…+2632+2642 = 802,010 = 2652+2662+…+2742+2752.

 

802,725

[Math.]  A pair of amicable numbers (802725, 863835).

 

803,760 & 803,761

[Math.]  The 8th square number that is the sum of squares of 2 consecutive numbers: 1,292,061,882,721 = 1,136,6892 = 8037602+8037612. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 52, 292, 1692, 9852...

Or in other words: (803,760, 803,761, 1,136,689) is the 8th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

 

804,357

[Math.]  804,357 = (80+4–3+5+7)3 = 933.

 

806,404

[Math.]  (121+878 = 999 = 101+898)

1212 = 014,641 & 014+641 = 655

8782 = 770,884 & 770+884 = 1654 and 1+654 = 655.

and

1012 = 010,201 & 010+201 = 211

8982 = 806,404 & 806+404 = 1210 and 1+210 = 211.

 

809,523

[Math.]  Multiples of 047619 (= 095238/2) by 2, 5, 8, 11, 17 and 20 yield all 6 rotations of the digits of 095238 (the period of the rational number 2/21 = 0.095238095238… or 0.095238): 095238, 238095, 380952, 523809, 809523 and 952380, respectively.