Numbers 920,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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923,076

[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.

[Math.]  230,769×4 = 923,076.

[Math.]  307,692×3 = 923,076.

923,594

[Math.]  1,518,037,444 = (1518+037444)2 = 38,9622 and

923,594,037,444 = (923594+037444)2 = 961,0382 and 38962+961038 = 1,000,000.

925,765

[Math.]  One of Markov numbers are… 75025, 96557, 135137, 195025, 196418, 294685, 426389, 499393, 514229, 646018, 925765…

925,993

[Math.]  The 34th Keith number.

926,835

[Math.]  Two consecutive sums of consecutive numbers:

9409+…+9506 = 9507+…+9603 = 926,835.

926,884

[Math.]  A base system of multigrade equalities: (

1+5+10+18+23+27 = 84 = 2+3+13+15+25+26

12+52+102+182+232+272 = 1,708 = 22+32+132+152+252+262

13+53+103+183+233+273 = 38,808 = 23+33+133+153+253+263

14+54+104+184+234+274 = 926,884 = 24+34+134+154+254+264

15+55+105+185+235+275 = 22,777,944 = 25+35+135+155+255+265

Multigrade equalities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

923,076

[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.

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References [20]