Numbers 790,000,000s

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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790,123,456

[Math.]  012345679 is the 9-digit period of the rational number 1/81 = 0.012345679012345679… or 0.012,345,679.

Multiples of 012345679 by 1, 10, 19, 28, 37, 46, 55, 64 and 73 yield all 9 digit-rotations of the number itself: 012,345,679, 123,456,790, 234,567,901, 345,679,012, 456,790,123, 567,901,234, 679,012,345, 790,123,456 and 901,234,567. All numbers are missing digit 8.

Multiples of 012345679 by a number from 1 to 80 of the form x (mod 9), where x = 1, 2, 4, 5, 7 or 8, will yield a 9-digit number, including all but one digit from 0 to 9. The missing digit is (9–x), again taking only values: 8, 7, 5, 4, 2 or 1. (Adding extra 0 to any 8-digit numbers). Its multiple by 81 is 999,999,999.

[Math.]  Number 098,765,432 misses one digit 1 in 10 digits 0-9:

098,765,432´2 = 197,530,864 misses one digit 2 (modulo 9)

098,765,432´4 = 395,061,728 misses one digit 4 (modulo 9)

098,765,432´5 = 493,827,160 misses one digit 5 (modulo 9)

098,765,432´7 = 691,358,024 misses one digit 7 (modulo 9)

098,765,432´8 = 790,123,456 misses one digit 8 (modulo 9)

and 098,765,432×9 = 888,888,888.

793,605,241

[Math.] 281712 = 793,605,241, a square using all 9 digits 0-9 once, except digit 8.

795,409,209

[Math.] Sum of the first 237 cube numbers:

13+23+…+2373 = 795,409,209 = (1+2+…+237)2 = 28,2032.

798,401,536

[Math.] 282562 = 798,401,536, a square using all 9 digits 0-9 once, except digit 2.

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.