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From Wikipedia, the free encyclopedia

149 (one hundred [and] forty-nine) is the natural number between 148 and 150. It is also a prime number.

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Contents

In mathematics

149 is the 35th prime number, and with the next prime number, 151, is a twin prime, thus 149 is a Chen prime.[1]

149 is an emirp, since the number 941 is also prime.[2]

149 is a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes.

149 is an irregular prime since it divides the numerator of the Bernoulli number B130.

149 is an Eisenstein prime with no imaginary part and a real part of the form .

The repunit with 149 1s is a prime in base 5 and base 7.

Given 149, the Mertens function returns 0.[3] It is the third prime having this property.[4]

149 is a tribonacci number, being the sum of the three preceding terms, 24, 44, 81.[5]

149 is a strictly non-palindromic number, meaning that it is not palindromic in any base from binary to base 147. However, in base 10 (and also base 2), it is a full reptend prime, since the decimal expansion of 1/149 repeats 006711409395973154362416107382550335570469798657718120805369127516778523489932885906040268 4563758389261744966442953020134228187919463087248322147651 indefinitely.

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In transportation

In other fields

149 is also:

See also

References

  1. ^ "Sloane's A109611 : Chen primes: primes p such that p + 2 is either a prime or a semiprime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  2. ^ "Sloane's A006567 : Emirps". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  3. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
  4. ^ "Sloane's A100669 : Zeros of the Mertens function that are also prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  5. ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.

External links

This page was last edited on 8 July 2019, at 19:28
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