Numbers 210,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

[1M] & [10M] & [100M- [200M] - [300M] - [400M] - [500M] - [600M] - [700M] - [800M] - [900M]  & [1B]

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211,266,225

[Math.] Sum of the first 170 cube numbers:

13+23+…+1703 = 211,266,225 = (1+2+…+170)2 = 14,5352.

212,890,625

[Math.]  An automorphic number, whose powers end with the number itself. It is extracted from a 17-digit automorphic number 56,259,918,212,890,625, which remains automorphic when dropping the left-most digits.

214,358,881

[Math.]  118 = 214,358,881 and 21–4+3–5+8–8+8–1 = 22 = 11×2.

215,384,976

[Math.]  146762 = 215,384,976, one of thirty 9-digit square numbers using all 9 digits 1-9 once.

216,266,436

[Math.]  Sum of the first 171 cube numbers:

13+23+…+1713 = 216,266,436 = (1+2+…+171)2 = 14,7062.

217,356,049

[Math.]  147432 = 217,356,049, a square using all 9 digits 0-9 once, except digit 8.

218,034,756

[Math.]  147662 = 218,034,756, one of 22 squares using all 9 digits 0-8 once.

219,999,978

[Math.]

(*)   8712 = 2178×4 & 8712×2178 = 18,974,736 = 43562 (= 664)

8712…8712 = 2178…2178×4 & 8712…8712×2178…2178 = 4356…43562.

(**)   87912 = 21978×4 & 21978×87912 = 1,932,129,936 = 439562

87912…87912 = 21978…21978×4 & 21978…21978×87912…87912 = 43956…439562.

(***)   879999912 = 219999978×4 & 219999978×879999912 = 4399999562

879999912…879999912 = 219999978…219999978×4 &

219999978…219999978×879999912…879999912 = 439999956…4399999562.

(****)   879…912 = 219…978×4 & 219…978×879…912 = 439…9562

879…912…879…912 = 219…978…219…978×4 &

219...978...219...978×879...912...879...912 = 439...956...439...9562.

...

xyz,abc,def

[Math.]  For any xyz = 100 to 999, there are always six 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 6 digit-rotations of 142,857 and the number  xyz,abc,def is a multiple of 142,857.

For any xyz = 100 to 999, there are always twelve 6-digit numbers abc,edf such that the sum (xyz+abc,def) is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number xyz,abc,def is a multiple of 76,923.