91 (number)
91 (ninety-one) is the natural number following 90 and preceding 92.
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Look up ninety-one in Wiktionary, the free dictionary. |
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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
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 Missile 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
- "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- "Sloane's A003215 : Hex (or centered hexagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- "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.
- "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- Friedman, Erich. What's Special About This Number?
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