49 (number)

Last updated
48 49 50
Cardinal forty-nine
Ordinal 49th
(forty-ninth)
Factorization 72
Divisors 1, 7, 49
Greek numeral ΜΘ´
Roman numeral 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.

Contents

In mathematics

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

49 has an aliquot sum of 8; itself a prime power, and hence an aliquot sequence of two composite members (49, 8, 7,1,0).

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).

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

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

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 (note that this number is the period) positive integers that are less than 49 and coprime to 49. 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 149 satisfies:

In chemistry

In astronomy

In religion

In sports

In music

In other fields

Forty-nine is:

See also

Related Research Articles

2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures.

15 (fifteen) is the natural number following 14 and preceding 16.

21 (twenty-one) is the natural number following 20 and preceding 22.

<span class="mw-page-title-main">Square number</span> Product of an integer with itself

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.

45 (forty-five) is the natural number following 44 and preceding 46.

25 (twenty-five) is the natural number following 24 and preceding 26.

28 (twenty-eight) is the natural number following 27 and preceding 29.

38 (thirty-eight) is the natural number following 37 and preceding 39.

27 is the natural number following 26 and preceding 28.

76 (seventy-six) is the natural number following 75 and preceding 77.

81 (eighty-one) is the natural number following 80 and preceding 82.

86 (eighty-six) is the natural number following 85 and preceding 87.

37 (thirty-seven) is the natural number following 36 and preceding 38.

39 (thirty-nine) is the natural number following 38 and preceding 40.

55 (fifty-five) is the natural number following 54 and preceding 56.

62 (sixty-two) is the natural number following 61 and preceding 63.

65 (sixty-five) is the natural number following 64 and preceding 66.

68 (sixty-eight) is the natural number following 67 and preceding 69. It is an even number.

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.

99 (ninety-nine) is the natural number following 98 and preceding 100.

References

  1. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. 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.
  3. Hecker, S.S. (2000). "Plutonium: an historical overview. In: Challenges in Plutonium Science". Los Alamos Science. 26 (1): 1–2.
  4. "Days of Forty-Nine, The". California State University, Fresno . Retrieved 2022-10-09.
  5. "RN2803: Days of '49". English Folk Dance and Song Society . Retrieved 2022-10-09.
  6. "Forty-nine dance". Encyclopedia Britannica . Retrieved May 25, 2018.