Numbers 930,000,000s

938,074,384

[Math.]  Sum of the first 247 cube numbers:

13+23+…+2473 = 938,074,384 = (1+2+…+247)2 = 30,6282.

 

938,271,604

[Math.]  Multiples of 012345679 by 4, 13, 22, 31, 40, 49, 58, 67 and 76 will yield all 9 rotations of 049382716: 049382716, 160493827, 271604938, 382716049, 493827160, 604938271, 716049382, 827160493 and 938271604. All numbers are missing digit 5. 

 

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.