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Numbers 14,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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 14,068 & 14,132

[Math.]  The only equation of this form: 140685+62375+50275 = 141325+2205, where its largest entry is less than 20,000 (found by Bob Scher, 1995).

 

14,080

[Music]   A frequency (Hz, Hertz) of the musical note A (La):

A0 = 27.5 Hz, A1 = 55 Hz, A2 = 110 Hz, A3 = 220 Hz, A4 = 440 Hz, A5 = 880 Hz, A6 = 1760 Hz,  A7 = 3520 Hz, A8 = 7040 Hz, A9 = 14,080 Hz and A10 = 28,160 Hz.

 

[Zip]  U.S. Postal Zip Code: Holland, New York  11080.

 

 14,098

[Math.]  140982 = 198,753,604, a square using all 9 digits 0-9 once, except digit 2.

 

14,141

[Math.]  14141 = 179×79.

 

14,159

[Math.]  A prime number, formed by the first 5 decimal digits of the number p = 3.141 592 653…

 

14,264 & 14,288

[Math.]  The first known sociable number chain (by Poulet, 1918):

12496 → 14288 → 15472 → 14536 → 14264 → 12496.

 

14,285

[Math.]

1×7 + 3 = 10

14×7 + 2 = 100

142×7 + 6 = 1000

1428×7 + 4 = 10000

14285×7 + 5 = 100000

142857×7 + 1 = 1000000

 

1428571×7 + 3 = 10000000

14285714×7 + 2 = 100000000

142857142×7 + 6 = 1000000000

1428571428×7 + 4 = 10000000000

14285714285×7 + 5 = 100000000000

142857142857×7 + 1 = 1000000000000

 

1428571428571×7 + 3 = 10000000000000

...

 

14,316

[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)

 

14,322

[Math.]  The denominator of the 30th Bernoulli number:  B30 = 8615841276005/14322.

 

14,400

[Math.]  Sum (in degrees) of all internal angles of an 82-side polygon.

 

[Math.]  Four square numbers using the same digits: 1022 = 10404, 1202 = 14400, 2012 = 40401 and 2102 = 44100.

 

 [Math.]  Sum of the first 15 cube numbers:

13+23+33+…+133+143+153 = 14,400 = (1+2+3+…+13+14+15)2 = 1202. 

 

[Tech.]  One of standardized baud rate (bits per second) in electronic data transmissions.

 

 14,442

[Math.]  144422 = 208,571,364, one of 22 squares using all 9 digits 0-8 once.

 

14,536

[Math.]  The first known sociable number chain (by Poulet, 1918): 12496 → 14288 → 15472 → 14536 → 14264 → 12496.

 

14,538

[Math.]  Each ratio 14538/7269 = 2, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.

 

14,586

[Math.]  Each ratio 14586/7293 = 2, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.

 

14,595

[Math.]  A pair of all-odd amicable numbers (12285, 14595).

 

14,607

[Math.]  Two multiples of number 4869, 4869×3 = 14,607 and 4869×8 = 38,952, use each of 10 digits 0-9 once.

 

14,641

[Math.]  14,641 = (14–6+4–1)4 = 114.

 

 [Math.]  (121+878 = 999 = 101+898)

1212 = 014,641 & 014+641 = 6555

8782 = 770,884 & 770+884 = 1654 and 1+654 = 655.

and

1012 = 010,201 & 010+201 = 211

8982 = 806,404 & 806+404 = 1210 and 1+210 = 211

 

14,658

[Math.]  Each ratio 14658/7329 = 2, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #2.

 

14,676

[Math.]  146762 = 215,384,976, one of thirty 9-digit square numbers using each of 9 digits 1-9 once.

 

14,685

[Math.]  The ratio 14685/2937 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

14,700

[Math.]  Two consecutive sums of consecutive numbers:

576+577+…+600 = 601+602+…+624 = 14,700.

 

14,701

[Math.]  One of Markov numbers are… 4181, 5741, 6466, 7561, 9077, 10946, 14701, 28657, 33461, 37666, 43261, 51641, 62210, 75025, 96557…

 

14,743

[Math.]  147432 = 217,356,049, a square using all 9 digits 0-9 once, except digit 2.

 

14,766

[Math.]  147662 = 218,034,756, one of 22 squares using all 9 digits 0-8 once.

 

14,833

[Math.]  Subfactorial of 8 is !8 = 14833.

 

14,835

[Math.]  The ratio 14835/2967 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

[Math.]  Two multiples of number 2967, 2967×5 = 14,835 and 2967×7 = 20,769, use each of 10 digits 0-9 once.

 

14,865

[Math.]  The ratio 14865/2973 = 5, using each of 9 digits 1-9 once, shows how to arrange a 9-book set on 2 shelves to mark the book #5.

 

14,869

[Math.]  3,122,490 = 2×3×5×7×14869, whose prime factors use each of 9 digits 1-9 once.

 

14,884

[Math.]  Reversible numbers and their squares: 1222 = 14884 and 2212 = 48841.

 

14,940

[Math.]  Sum (in degrees) of all internal angles of an 85-side polygon.

A regular 85-side polygon is constructible by using only straightedge and compass.

 

14nnn

[Zip]  U.S. Postal Zip Codes of New York: 10nnn-14nnn and 005nn.