Pernicious number

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In number theory, a pernicious number is a positive integer such that the Hamming weight of its binary representation is prime. [1]

Contents

Examples

The first pernicious number is 3, since 3 = 112 and 1 + 1 = 2, which is a prime. The next pernicious number is 5, since 5 = 1012, followed by 6, 7 and 9. [2]

Properties

Related Research Articles

In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.

<span class="mw-page-title-main">Perfect number</span> Integer equal to the sum of its proper divisors

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<span class="mw-page-title-main">Power of two</span> Two raised to an integer power

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73 (seventy-three) is the natural number following 72 and preceding 74. In English, it is the smallest natural number with twelve letters in its spelled out name.

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The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Sloane is chairman of the OEIS Foundation.

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<span class="mw-page-title-main">Centered nonagonal number</span> Centered figurate number that represents a nonagon with a dot in the center

A centered nonagonal number is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for n layers is given by the formula

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In mathematics, a pandigital number is an integer that in a given base has among its significant digits each digit used in the base at least once. For example, 1234567890 is a pandigital number in base 10. The first few pandigital base 10 numbers are given by :

In number theory, an odious number is a positive integer that has an odd number of 1s in its binary expansion.

References

  1. ↑ Deza, Elena (2021), Mersenne Numbers And Fermat Numbers, World Scientific, p. 263, ISBN   9811230331
  2. 1 2 3 Sloane, N. J. A. (ed.), "SequenceA052294", The On-Line Encyclopedia of Integer Sequences , OEIS Foundation
  3. ↑ Colton, Simon; Dennis, Louise (2002), "The NumbersWithNames Program", Seventh International Sumposium on Artificial Intelligence and Mathematics
  4. ↑ Cai, Tianxin (2022), Perfect Numbers And Fibonacci Sequences, World Scientific, p. 50, ISBN   981124409X
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