49 (number)

← 48 49 50 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-nine
Ordinal	49th (forty-ninth)
Factorization	72
Divisors	1, 7, 49
Greek numeral	ΜΘ´
Roman numeral	XLIX, xlix
Binary	1100012
Ternary	12113
Senary	1216
Octal	618
Duodecimal	4112
Hexadecimal	3116

49 (forty-nine) is the natural number following 48 and preceding 50.

In mathematics

Forty-nine is the square of the prime number seven and hence the fourth non-unitary square prime of the form p².

It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these). ^[1]

Along with the number that immediately derives from it, 77, the only number under 100 not having its home prime known (as of 2016 ^[update] ).

The smallest triple of three squares in arithmetic succession is (1,25,49), and the second smallest is (49,169,289).

49 is the smallest discriminant of a totally real cubic field. ^[2]

49 and 94 are the only numbers below 100 whose all permutations are composites but they are not multiples of 3, repdigits or numbers which only have digits 0, 2, 4, 5, 6 and 8, even excluding the trivial one digit terms.

49 = 7^2 and 94 = 2 * 47

The number of prime knots with 9 crossings is 49. ^[3]

Decimal representation

The sum of the digits of the square of 49 (2401) is the square root of 49.

49 is the first square where the digits are squares. In this case, 4 and 9 are squares.

Reciprocal

See also: Repeating decimal

The fraction ⁠1/49⁠ is a repeating decimal with a period of 42:

⁠1/49⁠ = 0.0204081632 6530612244 8979591836 7346938775 51 (42 digits repeat)

There are 42 positive integers less than 49 and coprime to 49. (42 is the period.) Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a cyclic permutation of the original number:

• 020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102
• 020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653
• 020408163265306122448979591836734693877551 × 4 = 081632653061224489795918367346938775510204
• ...

The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right:

02   04     08       16         32           64            128              256                512                 1024                   2048 +                   ... ---------------------- 020408163265306122448979591836734693877551...0204081632...

because 1⁄49 satisfies:

${\displaystyle x={\frac {1}{50}}+{\frac {2x}{100}}={\frac {1}{50}}(1+x)\,.}$

In chemistry

• During the Manhattan Project, plutonium was also often referred to simply as "49". Number 4 was for the last digit in 94 (atomic number of plutonium) and 9 for the last digit in Pu-239, the weapon-grade fissile isotope used in nuclear bombs. ^{[4] [5]}

In religion

• In Judaism: the number of days of the Counting of the Omer and the number of years in a Jubilee (biblical) cycle.
• In Buddhism, 49 days is one of the lengths of the intermediate state (bardo)

In other fields

Forty-nine is:

• 49er , one who participated in the 1849 California Gold Rush. This meaning has endured and things continue to be referred to as "49er," such as a member of the San Francisco 49ers team of the National Football League.
• A 49 is a party after a powwow or any gathering of American Indians, held by the participants. It is also type of song that is sung on such occasions. A 49 is typically held in an isolated place and features drumming and singing. ^[6]

References

1. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. Sloane, N. J. A. (ed.). "SequenceA006832(Discriminants of totally real cubic fields.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-03-20.
3. Sloane, N. J. A. (ed.). "SequenceA002863(Number of prime knots with n crossings)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Hammel, E.F. (2000). "The taming of "49" — Big Science in little time. Recollections of Edward F. Hammel, pp. 2-9. In: Cooper N.G. Ed. (2000). Challenges in Plutonium Science" (PDF). Los Alamos Science . 26 (1): 2–9.
5. Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science. 26 (1): 1–2.
6. "Forty-nine dance". Encyclopedia Britannica . Retrieved May 25, 2018.