91 (number)

91 (ninety-one) is the natural number following 90 and preceding 92.

← 90 91 92 →
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Cardinal	ninety-one
Ordinal	91st (ninety-first)
Factorization	7 × 13
Divisors	1, 7, 13, 91
Greek numeral	ϞΑ´
Roman numeral	XCI
Binary	10110112
Ternary	101013
Octal	1338
Duodecimal	7712
Hexadecimal	5B16

In mathematics

91 is:

• the twenty-seventh distinct semiprime and the second of the form (7.q).
• a triangular number.
• a hexagonal number,[1] one of the few such numbers to also be a centered hexagonal number.[2]
• a centered nonagonal number.[3]
• a centered cube number.[4]
• a square pyramidal number, being the sum of the squares of the first six integers.[5]
• the smallest positive integer expressible as a sum of two cubes in two different ways if negative roots are allowed (alternatively the sum of two cubes and the difference of two cubes): 91 = 6³ + (−5)³ = 4³ + 3³. (See 1729 for more details). This implies that 91 is the second cabtaxi number.
• the smallest positive integer expressible as a sum of six distinct squares: 91 = 1² + 2² + 3² + 4² + 5² + 6². The only other ways to write 91 as a sum of distinct squares are: 91 = 1² + 4² + 5² + 7² and 91 = 1² + 3² + 9².
• the smallest pseudoprime satisfying the congruence 3ⁿ ≡ 3 mod n.[6]
• a repdigit in base 9 (111₉).
• palindromic in bases 3 (10101₃), 9 (111₉), and 12 (77₁₂).
• the fourth composite number in the 11-aliquot tree. The aliquot sum of 91 is 21 within the aliquot sequence (91,21,11,1,0).

The decimal equivalent of the fraction ​¹⁄₉₁ can be obtained by using powers of 9.

In science

• 91 is the atomic number of protactinium, an actinide.
• McCarthy 91 function, a recursive function in discrete mathematics
• Messier object M91, a magnitude 11.5 spiral galaxy in the constellation Coma Berenices
• The New General Catalogue object NGC 91, a single star in the constellation Andromeda

In other fields

See also: List of highways numbered 91

Ninety-one is also:

• The code for international direct dial phone calls to India
• In cents of a U.S. dollar, the amount of money one has if one has one each of the coins of denominations less than a dollar (penny, nickel, dime, quarter and half dollar)
• The ISBN Group Identifier for books published in Sweden.
• Psalm 91 is known as the Psalm of Protection. It is also the title of a book by Peggy Joyce Ruth
• 91 is a solitaire card game where the object is to move cards, so the top cards total 91.
• STS-91 Space Shuttle Discovery mission to the International Space Station, June 2, 1998
• Swedish comic strip 91:an
• The 91st Space Wing (91 SW) is a Minuteman (missile) III unit of the United States Air Force, based at Minot Air Force Base, North Dakota
• The number of the French department Essonne
• Ninety One or 91 is a Kazakhstan Q-pop boy band formed by JUZ Entertainment in 2014

References

1. "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
2. "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
3. "Sloane's A060544 : Centered 9-gonal (also known as nonagonal or enneagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
4. "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
5. "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
6. Friedman, Erich. What's Special About This Number?