Numbers 1,100,000,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

1,000,000,0001,100,000,0001,200,000,0001,300,000,0001,400,000,000

1,500,000,0001,600,000,0001,700,000,0001,800,000,000 – 1,900,000,000

[1B] – [2B] – [3B] – [4B] – [5B] – [6B] – [7B] – [8B]  – [9B] & [10B]

1  - 10 - 100  - 1000 - 10,000 - 100,000 - 1M - 10M - 100M1B10B - 100B - 1T - 10T - 100T - 1Q ...

1,111,022,224

[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.

33,332= 1111022224 & 11,110+22,224 = 33,334 = 33,332+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.

1,111,111,111 (separate page)

1,111,122,222, 1,111,155,555, 1,111,188,888

1,111,222,221, 1,111,555,551 & 1,111,888,881

[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

 33333×33334 = 1111122222 33333×33335 = 1111155555 33333×33336 = 1111188888 33333×33337 = 1111222221 33333×33347 = 1111555551 33333×33357 = 1111888881

… (generalizable pattern) …

1,111,155,556

[Math.]   Repeatedly inserting numbers 15 in the middle of the square number 16 yields other squares 1156 = 342, 111556 = 3342, 11115556 = 33342, 1111155556 = 333342

1,111,222,225

[Math.]   Repeatedly inserting numbers 12 between the digits 1 and 2 in the square number 1225 = 352 yields other squares 112225 = 3352, 11122225 = 33352, 1111222225 = 333352

1,115,157,653

[Math.]    10373 = 1,115,157,653 = (1115+1+5–76–5–3)3.

1,116,294,921

[Math.]   Sum of the first 258 cube numbers:

13+…+2583 = 1,116,294,921 = (1+2+…+258)2 = 33,4112.

1,119,638,521

[Math.]  The 6th square number that is the sum of squares of 2 consecutive numbers: 334612 = 1,119,638,521 = 236602+236612. Each root number in the series is 6 times the previous root number minus the earlier root number: 1, 52, 292, 1692, 9852

Or in other words:

(23660, 23661, 33461) is the 6th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

1,122,332,211

[Math.]

11×11 = 121

112,211×11 = 1,234,321

1,122,332,211×11 = 12,345,654,321

11,223,344,332,211×11 =  123,456,787,654,321

112,233,445,544,332,211×11  = 1,234,567,900,987,654,321

...

1,123,581,321

[Math. & Literature]   A sequence of first 8 consecutive Fibonacci numbers used in Dan Brown’s book “The Da Vinci Code” as a bank account number.

1,133,668,900 (& 1,133,668,899)

[Math.]   Sum of the first 259 cube numbers:

13+…+2593 = 1,133,668,900 = = (1+2+…+259)2 = 33,6702 = 1,133,668,899+1.

1,134,903,170

[Math.]   The 45th Fibonacci number.  The first Fibonacci number greater than 1 billion.

1,150,653,920

[Math.]   1,150,653,920 =

= 116+215+314+413+512+611+710+89+98+107+116+125+134+143+152+161.

1,150,653,921

[Math.]  1,150,653,921 = 017+116+215+314+413+512++611+710+89+98+107+

+116+125+134+143+152+161+170.

1,151,244,900

[Math.]   Sum of the first 260 cube numbers:

13+…+2603 = 1,308,992,400 = (1+2+…+260)2 = 33,9302.

1,169,024,481

[Math.]   Sum of the first 261 cube numbers:

13+…+2613 = 1,169,024,481 = (1+2+…+261)2 = 34,1912.

1,187,009,209

[Math.]   Sum of the first 262 cube numbers:

13+…+2623 = 1,187,009,209 = (1+2+…+262)2 = 34,4532.

1,188,535,425

[Math.]   Two consecutive sums of consecutive square numbers:

1,188,535,425 = 48512+…+49002 = 49012+…+49492.

x,yzw,abc,def

[Math.]  For any x,yzw = 1000 to 9999, there are always six 6-digit numbers abc,edf such that x,yzw +abc,def is equal to one of 6 digit-rotations of 142,857 and the number x,yzw,abc,def is a multiple of 142,857.

For any x,yzw = 1000 to 9999, there are always twelve 6-digit numbers abc,edf such that x,yzw +abc,def is equal to one of 12 digit-rotations of 076,923 or 153,846 and the number x,yzw,abc,def is a multiple of 76,923.