230,769

[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.

[Math.]

230,769×4 = 923,076.

230,769×3 = 692,307.

076,923×3 = 230,769.

230,940

[Math.]  Sum (in degrees) of all internal angles of a 1285-side polygon.

A regular 1285-side polygon is constructible by using only straightedge and compass.

232,324

[Math.]  Square and cube of number 482 use different digits: 4822 = 232,324 and 4823 = 111,980,168.

232,593

[Math.] Two consecutive sums of consecutive numbers: 3721+…+3782 = 3783+…+3843 = 232,593.

232,768 & 232,769

[Math.] 232,768 = 111+210+39+48+57+66+75+84+93+102+111.

232,769 = 012+111+210+39+48+57+66+75+84+93+102+111+120.

233,993

[Math.]  A right-truncatable prime number: self, 23399, 2339, 233, 23 and 2 are prime numbers.

234,256

[Math.]  224 = 234,256 = (2+3+4+2+5+6)4

23+42+56 = 65+24+32 = 121 = 112.

234,569

[Math.] Number 234,569 misses 3 digits 1, 7 and 8 in 9 digits 0-9.

234,569×2 = 469,138 misses 3 digits 2, 5 and 7 (modulo 9)

234,569×4 = 938,276 misses 3 digits 4, 1 and 5 (modulo 9).

234,579

[Math.]  Number 234,579 misses 3 digits 1, 6 and 8 in 9 digits 0-9.

234,579×2 = 469,158 misses 3 digits 2, 3 and 7 (modulo 9).

234,589

[Math.]  A prime number.

Number 234,589 misses 3 digits 1, 6 and 7 in 9 digits 0-9.

234,589×2 = 469,178 misses 3 digits 2, 3 and 5 (modulo 9).

234,679

[Math.]  Number 234,679 misses 3 digits 1, 5 and 8 in 9 digits 0-9.

234,679×2 = 469,358 misses 3 digits 2, 1 and 7 (modulo 9)

234,679×4 = 938,716 misses 3 digits 4, 2 and 5 (modulo 9).

234,689

[Math.]  Number 234,689 misses 3 digits 1, 5 and 7 in 9 digits 0-9.

234,689×2 = 469,378 misses 3 digits 2, 1 and 5 (modulo 9)

234,689×4 = 938,756 misses 3 digits 4, 2 and 1 (modulo 9).

234,789

[Math.]  Number 234,789 misses 3 digits 1, 5 and 6 in 9 digits 0-9.

234,789×2 = 469,578 misses 3 digits 2, 1 and 3 (modulo 9).

235,416

[Math.]  The 8th square number that is also a triangular number: 235,4162 = 1+2+…+332,928 = 55,420,693,056. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 62, 352, 2042, 11892

235,813

[Math.]  A prime number, formed by 5 consecutive Fibonacci numbers 2, 3, 5, 8 and 13.

235,951

[Trivia]  The largest prime number that can be displayed on a digital clock in the 24-hour format (excluding the colon “:”) is 23:59:51.

235,959

[Trivia] The largest number that can be displayed on a digital clock in the 24-hour format (excluding the colon “:”) is 23:59:59.

235,678

[Math.] Number 235,678 misses 3 digits 1, 4 and 9 in 9 digits 1-9:

235,678×2 = 471,356 misses 3 digits 2, 8 and 9 (modulo 9).

238,095

[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.]  238,095×4 = 952,380.

238,328

[Math.]  238,328 = (23+8+3+28)3 = 623.

238,854

[Astronomy]  The distance (miles) between center of the Earth and center of the Moon.

(to be checked)

239,933

[Math.]  A right-truncatable prime number: self, 23993, 2399, 239, 23 and 2 are prime numbers.