Numbers 300,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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300,000 (separate page)

307,530

[Math.]  Two consecutive sums of consecutive numbers:

4489+…+4556 = 4557+…+4623 = 307,530.

307,692

[Math.]  Multiples of 076923 (the period of the rational number 1/13 = 0.076923076923… or 0.076923) by 3, 4, 9, 10 and 12 yield 5 other digit-rotations of the number itself: 230769, 307692, 692307, 769230 and 923076, respectively.

307,692

[Math.]  A 3-pseudoparasite-double number: 307,692×3 = 923,076.

A 4-pseudoparasite number: 076,923×4 = 307,692. Or generalized to:

[Math.]  The 6-digit period of the rational number 1/13 = 0.076923076923… or 0.076923. Its multiple by 13 is 999,999.  Then,   076,923×n = abc,def,ghi,jkl and

 abc,def+ghi,jkl = 076,923, if n  = 13t+1 abc,def+ghi,jkl = 692,307, if n  = 13t+9 abc,def+ghi,jkl = 230,769, if n  = 13t+3 abc,def+ghi,jkl = 769,230, if n  = 13t+10 abc,def+ghi,jkl = 307,692, if n  = 13t+4 abc,def+ghi,jkl = 923,076, if n  = 13t+12

for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923.

And 076,923×n = abc,def,ghi,jkl &

 abc,def+ghi,jkl = 153,846, if n  = 13t+2 abc,def+ghi,jkl = 538,461, if n  = 13t+7 abc,def+ghi,jkl = 384,615, if n  = 13t+5 abc,def+ghi,jkl = 615,384, if n  = 13t+8 abc,def+ghi,jkl = 461,538, if n  = 13t+6 abc,def+ghi,jkl = 846,153, if n  = 13t+11

for t = 0 to 76,922, and in fact abc,edf = t.  The results are digit-rotations of 076,923×2 = 153,846. It is the period of the rational number 2/13 = 0.153846153846… or 0.153846), and the sums of first and last 3-digit numbers are always 999.

308,085

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

1712+1722+…+1792+1802 = 308, 085 = 1812+1822+…+1882+1892.

308,620

[Math.]  A pair of amicable numbers (308620, 389924).

309,136

[Math.]  1122 = 012,544 & 012+544 = 556 & 5562 = 309,136 & 309+136 = 445 & 4452 = 198,025 & 198+025 = 223 & 2232 = 049,729 & 049+729 = 778 & 7782 = 605,284 & 605+284 = 889 & 8892 = 790,321 & 790+321 = 1111. Also in the same pattern: 3342 = 111556 & 111+556 = 667.