Numbers 11,000s

A page of the Numeropedia - the Special Encyclopedia of Numbers

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11,000

[EECS]  11K(W) is one of standard numerical values for resistors (of tolerance class 5%).

[Geology]  Michigan has more than 11,000 inland lakes and is also called itself “Wonderland of 11,000 Lakes” to top Minnesota, known as “Land of 10,000 Lakes”, even though Minnesota actually have more than 12,000 lakes.

11,025

[Math.]  Sum of the first 14 cube numbers:

13+23+33+…+123+133+143 = 11,025 = (1+2+3+…+12+13+14)2 = 1052.

11,111

[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.

11,171

[Math.]  A sequence of prime numbers of similar pattern: 11171, 10181, 9181, 8171, 7151, 6121 and 5081, whose differences are 990, 1000, 1010, 1020, 1030 and 1040, respectively.

11,191

[Math.]  11191 = 192×31.

11,200

[Science]  The “Escape Velocity” from the Earth: 11,200 meters/second.

11,213

[Math.]  A prime number. A Mersenne exponent: 211213–1 is the 23rd Mersenne prime number.

11,301

[Math.]  10311 (a deficient number) has 7 divisors, excluding itself: 1, 3, 7, 21, 491, 1473 and 3437, whose digit-reversal numbers add up to the digit-reversal of the number 10311: 11301 = 1+3+7+12+194+3741+7343. (Joseph L. Pe, Picture-Perfect Numbers and other Digit-Reversal Diversions, 2002).

11,377

[Math.]  11377 = 19+28+37+46+55+64+73+82+91.

11,378

[Math.]  11,378 = 010+19+28+37+46+55+64+73+82+91+100.

11,385

[Math.]  Two consecutive sums of consecutive numbers: (smallest 5-digit):

484+485+…+506 = 507+508+…+528 = 11,385.

11,500

[Math.]  A base system of multigrade equalities: (References [26])

1+15+22+50+57+71 = 2+11+27+45+61+70 = 5+6+35+37+66+67 = 216

12+152+222+502+572+712 = 22+112+272+452+612+702

= 52+62+352+372+662+672 = 11,500

13+153+223+503+573+713 = 23+113+273+453+613+703

= 53+63+353+373+663+673 = 682,128

14+154+224+504+574+714 = 24+114+274+454+614+704

= 54+64+354+374+664+674 = 42,502,564

15+155+225+505+575+715 = 25+115+275+455+615+705

= 55+65+355+375+665+675 = 2,724,334,416.

Multigrade equatlities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

11,664

[Math.]  Three square numbers using the same digits: 1082 = 11664, 1292 = 16641 and 2042 = 41616.

11,777

[Math.]  Surrounding the number 777 with number 11 forms some prime numbers: 11777, 77711, 11777711 and 11117771111.

11,826

[Math.]  118262 = 139,854,276, one of thirty 9-digit square numbers using each of 9 digits 1-9 once. (The smallest such number).

11,881

[Math.]  (Sequence of numbers 10…09).

11,881 = (118–8–1)2 = 1092

11,939

[Math.]  Circular prime numbers: all 5 numbers 91193, 11939, 19391, 93911 and 39119 are prime. (They are all “emirp” numbers).

11,990

[Math.]  A base system of multigrade equalities: References [??])

1+4+12+13+20 = 50 = 2+3+10+16+19

12+42+122+132+202 = 730 = 22+32+102+162+192

13+43+123+133+203 = 11,990 = 23+33+103+163+193

Multigrade equalities still hold by adding any integer n to every base term in both sides.  Hence, the base equality always has number 1 appearing in one side.

11nnn

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

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References [26]