Numbers 380,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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380,952

[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.

 

[Math.]   095,238×4 = 380,952.

 

381,028  

[Math.]  The 2nd known amicable/sociable number chain: 14316 → 19116 → 31704 → 47616 → 83328 → 177792 → 295488 → 629072 → 589786 → 294896 → 358336 → 418904 → 366556 → 274924 → 275444 → 243760 → 376736 → 381028 → 285778 → 152990 → 122410 → 97946 → 48976 → 45946 → 22976 → 22744 → 19916 → 17716 → 14316. (of 28 links, currently the longest, found by Poulet, 1918)

 

381,060

[Math.]  Two consecutive sums of consecutive numbers:

5184+…+5256 = 5257+…+5328 = 381,060.

 

384,615

[Math.]  Multiples of 076923 (= 153846/2) by 2, 5, 6, 7, 8 and 11 yield all 6 different rotations of the digits of 153846 (the period of the rational number 2/13 = 0.135846153846… or 0.153846): 153846, 384615, 461538, 538461, 615384 and 846153.

 

385,000

[Astronomy]  The distance (km, kilometers) between center of the Earth and center of the Moon.

 

386,615

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.

 

389,924

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