34 (number)
| ||||
|---|---|---|---|---|
| Cardinal | thirty-four | |||
| Ordinal | 34th (thirty-fourth) | |||
| Factorization | 2 × 17 | |||
| Divisors | 1, 2, 17, 34 | |||
| Greek numeral | ΛΔ´ | |||
| Roman numeral | XXXIV | |||
| Binary | 1000102 | |||
| Ternary | 10213 | |||
| Senary | 546 | |||
| Octal | 428 | |||
| Duodecimal | 2A12 | |||
| Hexadecimal | 2216 | |||
34 (thirty-four) is the natural number following 33 and preceding 35.
In mathematics
34 is the ninth distinct semiprime[1] and has four divisors including one and itself. Specifically, 34 is the 9th distinct Semiprime, it being the 6th of the form (2.q).
Its neighbors, 33, and 35, also are distinct semiprimes, having four divisors each, and 34 is the smallest number to be surrounded by numbers with the same number of divisors as it has. This is the first distinct semiprime treble cluster[2] the next being 85, 86, 87.
The number 34 has an aliquot sum of 20, within an aliquot sequence of six composite numbers (34,20,22,14,10,8,7,1,0) to the Prime in the 7-aliquot tree.
It is the ninth Fibonacci number[3] and a companion Pell number.[4] Since it is an odd-indexed Fibonacci number, 34 is a Markov number,[5] appearing in solutions with other Fibonacci numbers, such as (1, 13, 34), (1, 34, 89), etc.
34 is the magic constant of a 4 by 4 normal magic square:[6]
This number is also the magic constant of n-Queens Problem for n = 4.[7]
34 is a heptagonal number.[8]
There are 34 topologically distinct convex heptahedra, excluding mirror images.[9]
There is no solution to the equation φ(x) = 34, making 34 a nontotient.[10] Nor is there a solution to the equation x − φ(x) = 34, making 34 a noncototient.[11]
It is an Erdős–Woods number.[12]
34 is a Reverse Anti-Gilda Number. Numbers whose Gilda Number-like Recursion is taken but first Sum of Digits is taken and then Absolute Value of (First Digit - Sum of Other Digits) is taken, then it gives its Reverse. Other Numbers like this are 0, 68, 293, 340, 472, 611, 680, 951, 2930, 3321, 3400, 4720, 6043, 6110, 6325, 6510, 6591, 6607, 6642, 6850, 9107, 9510, 9963, 15973, etc.
Sum of Digits of 34 = 3 + 4 = 7 First Digit - Sum of Other Digits = 3 - 4 = -1 Its Absolute Value = 1 7 + 1 = 8 1 + 8 = 9 8 + 9 = 17 9 + 17 = 26 17 + 26 = 43 = Reverse of 34
In science
- The atomic number of selenium
- Potentially one of the magic numbers in physics.[13][14]
- Messier object M34, a magnitude 6.0 open cluster in the constellation Perseus
- The New General Catalogue object NGC 34, a peculiar galaxy in the constellation Cetus
- The vertebral column is made up of up to 34 vertebrae.[15]
Literature
- In The Count of Monte Cristo, Number 34 is how Edmond Dantès is referred to during his imprisonment in the Château d'If.
Transportation
- 34th Street (Manhattan), a major cross-town street in New York City
- 34th Street (New York City Subway), multiple New York City subway stations
In other fields
34 is also:
- The traffic code of Istanbul, Turkey
- "#34", a song by the Dave Matthews Band
- The number of the French department Hérault
- +34 is the code for international direct-dial phone calls to Spain
- The number used to win the 2021 Daytona 500 with Michael McDowell and Front Row Motorsports. The number and team also won at Pocono Raceway with Chris Buescher and Talladega Superspeedway with David Ragan. In 1961, Wendell Scott won with the number to become the first African American to win in NASCAR.
See also
References
- ^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A056809". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A002203 : Companion Pell numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ Weisstein, Eric W. "Markov Number". mathworld.wolfram.com. Retrieved 2020-08-21.
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.
- ^ Sloane, N. J. A. (ed.). "Sequence A006003". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Counting polyhedra". Numericana. Retrieved 2022-04-20.
- ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A005278 : Noncototients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
- ^ "Sloane's A059756 : Erdős–Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2020-12-04.
- ^ "Evidence for a new nuclear 'magic number'" (Press release). Saitama, Japan: Riken. 2013-10-10. Retrieved 2013-10-14.
- ^ Steppenbeck, D.; Takeuchi, S.; Aoi, N.; et al. (2013-10-10). "Evidence for a new nuclear 'magic number' from the level structure of 54Ca". Nature. 502 (7470): 207–210. Bibcode:2013Natur.502..207S. doi:10.1038/nature12522. PMID 24108051. S2CID 205235415.
- ^ Jason M. Highsmith, MD (2020-03-03). "Spinal Anatomy Center". SpineUniverse. Retrieved 2022-08-10.
External links
- Prime Curios! 34 from the Prime Pages