Numbers 110,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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110,000

[EECS]  110K(W) is one of standard numerical values for resistors (of tolerance class 5%).

110,224

[Math.]  Square of numbers of similar pattern xxy, where y = x–1.

* 1102 = 012,100 & 012+100 = 112 = 110+2.

* 3322 = 110,224 & 110+224 = 334 = 332+2.

Similarly, 3…322 = 1…102…24 & 1…10+2…24 = 3…34 = 3…32+2.

* 4432 = 196,249 & 196+249 = 445 = 443+2

* 6652 = 442,225 & 442+225 = 667 = 665+2.

Similarly, 6…652 = 4…422…25 & 4…42+2…25 = 6…67 = 6…65+2.

* 7762 = 602,176 & 602+176 = 778 = 776+2.

110,503

[Math.]  A prime number.  A Mersenne exponent: 2110503–1 is the 29th Mersenne prime number.

110,889

[Math.]

121×(1+2+1) = 484 = 222

12,321×(1+2+3+2+1) = 110,889 = 3332

12,34,321×(1+2+3+4+3+2+1) = 19,749,136 = 4,4442

123,454,321×(1+2+3+4+5+4+3+2+1) = 3,086,358,025 = 55,5552

12,345,654,321×(1+2+3+4+5+6+5+4+3+2+1) = 444,443,555,556 = 666,6662

1,234,567,654,321×(1+2+3+4+5+6+7+6+5+4+3+2+1) =

= 60,493,815,061,729 = 7,777,7772

123,456,787,654,321×(1+2+3+4+5+6+7+8+7+6+5+4+3+2+1) =

= 7,901,234,409,876,544 = 88,888,8882

12,345,678,987,654,321×(1+2+3+4+5+6+7+8+9 +8+7+6+5+4+3+2+1) =

= 999,999,998,000,000,001 = 999,999,9992.

111,111

[Math.]  All numbers are palindromic.

 The 11th triangle number is 66 The 1111th triangle number is 617,716 The 111,111th triangle number is 6,172,882,716 The 11,111,111th triangle number is 61,728,399,382,716

[Math.]

1×1 = 1

11×11 = 121

111×111 = 12321

1111×1111 = 1234321

11111×11111 = 123454321

111111×111111 = 12345654321

1111111×1111111 = 1234567654321

11111111×11111111 = 123456787654321

111111111×111111111 = 12345678987654321

1111111111×1111111111 = 1234567900987654321.

1×9+2 = 11

12×9+3 = 111

123×9+4 = 1111

1234×9+5 = 11,111

12,345×9+6 = 111,111

123,456×9+7 = 1,111,111

1,234,567×9+8 = 11,111,111

12,345,678×9+9 = 111,111,111

123,456,789×9+10 = 1,111,111,111

1,234,567,900×9+11 = 11,111,111,111

...

[Math.]

3×37 = 111

33×3367 = 111,111

333×333667 = 111,111,111

3333×33336667 = 111,111,111,111

33333×3333366667 = 111,111,111,111,111

...

111,211

[Math.]  A sequence of prime numbers of similar pattern: 787, 9109, 111211 and 131413; or even as: 787, 091009, 111211 and 131413.

111,222, 111,555, 111,888, 112,221, 115,551 & 118,881

[Math.]

 33×34 = 1122 33×35 = 1155 33×36 = 1188 33×37 = 1221 33×47 = 1551 33×57 = 1881

 333×334 = 111,222 333×335 = 111,555 333×336 = 111,888 333×337 = 112,221 333×347 = 115,551 333×357 = 118,881

… (generalizable pattern) …

111,556

[Math.]  Repeatedly inserting numbers 15 in the middle of the square number 16 yields other squares 1156 = 342, 111556 = 3342, 11115556 = 33342

[Math.]  3342 = 111556 & 111+556 = 667. Also in a longer pattern:  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.

112,000--119,999 (separate page)