Numbers 1,300,000,000s

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 ...

1,303,210,000

[Math.]   (1+2+…+19)4 = [(15+25+…+195)+(17+27+…+197)]/2.

1,307,624,958 & 1,370,258,694

[Math.]

 Pan-digital number 2× a zero-less pan-digital number Uses each of 9 digits 1-9 once 1,037,246,958 = 2×518,623,479 = 9×57,624,831 1,046,389,752 = 2×523,194,876 = 9×58,132,764 1,286,375,904 = 2×643,187,952 = 9×71,465,328 1,307,624,958 = 2×653,812,479 = 9×72,645,831 1,370,258,694 = 2×685,129,347 = 9×76,125,483 1,462,938,570 = 2×731,469,285 = 9×81,274,365

1,311,738,121

[Math.]   The 12th square number that is the sum of squares of 2 consecutive numbers: 927,538,9202+927,538,9212 = 1,311,738,1212. 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:

(927,538,920, 927,538,921, 1,311,738,121) is the 12th Pythagorean triple (lengths of 3 sides of a right triangle), where 2 sides are consecutive integers.

1,313,547,925

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

1,313,547,925 = 50502+…+51002 = 51012+…+51502.

1,308,992,400

[Math.]   Sum of the first 269 cube numbers:

13+…+2693 = 1,308,992,400 = (1+2+…+269)2 = 36,1802.

1,318,820,881

[Math.]   508,853,9892 = 258,932,382,121,212,121

1,318,820,8812 = 1,739,288,516,161,616,161.

1,332,211,185

[Math.]   A secret code, using first 8 Fibonacci numbers in random order, used in Dan Brown’s book “The Da Vinci Code”.

1,333,333,334

[Math.]   1,333,333,334,666,666,667 = 1,333,333,3342–666,666,6672

=  (1333333334+666666667)×666666667.  (Generalizable).

1,338,462,225

[Math.]   Sum of the first 270 cube numbers:

13+…+2703 = 1,338,462,225 = (1+2+…+270)2 = 36,5852.

1,358,024,679

[Math.]   One of 27 special permutations of the pan-digital number 1,234,567,890: 123,456,789×11 = 1,358,024,679.

1,358,024,679

[Math.]   1,358,024,679´5,432,098,716 = 2,716,049,3582. Each number consists of all ten digits from 0 to 9.

1,358,364,736

[Math.]   Sum of the first 271 cube numbers:

13+…+2713 = 1,358,364,736 = (1+2+…+271)2 = 36,8562.

1,363,636,361

[Math.]   Repeatedly inserting numbers 36 in the middle of the prime number 11 yields other prime numbers: 1361, 136,361, 13,636,361, 1,363,636,361 and 136,363,636,361.

1,368,926,001

[Math.]

3692 = 136,161

36992 = 13682601

36,9992 = 1368926001

3699992 = 136899260001

36999992 = 13689992600001

369999992 = 1368999926000001

3699999992 = 136899999260000001

36999999992 = 13689999992600000001

3366992 = 113366,216601

336699992 = 11336688,32660001

33669999992 = 1133668899,3266000001

3366999999992 = 113366889999,326600000001

333,666,9992 = 111,333,666,221,666,001

333,666,999,9992 = 111,333,666,888,332,666,000,001

333,666,999,999,9992 = 111,333,666,888,999,332,666,000,000,001

3333,6666,99992 = 1111,3333,6666,2221,6666,0001

3333,6666,9999,99992 = 1111,3333,6666,8888,3332,6666,0000,0001

1,370,258,694 & 1,307,624,958 (see above)

1,375,298,099

[Math.]   245+285+675 = 35+545+625 = 1,375,298,099, sum of three 5th powers in 2 ways.

1,378,488,384

[Math.]   Sum of the first 272 cube numbers: 13+…+2723 = 1,378,488,384 = (1+2+…+272)2 = 37,1282.

1,382,054,976

[Math.]   371762 = 1,382,054,976, a square number using each of 10 digits 0-9 once. (The 8th of 87 such numbers).

1,398,834,801

[Math.]   Sum of the first 273 cube numbers:

13+…+2733 = 1,398,834,801 = (1+2+…+273)2 = 37,4012

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.