About the Number 31 (thirty-one)

MathBabbler was mathematizing the song "Mama Said" by the Shirelles (circa 1961) when he discovered that the Shirelles also did a song titled "31 Flavors" (circa 1963). He was working on "Obama Said" after having just completed a BAB titled "31% and 105% are Popular Percentages These Days."

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   31 is a natural, whole, integer
   31 is odd
   31 proper divisors are: 1,
   31 is deficient (sum of divisors is 1)
   31 is happy
   31 is not a Harshad number
   31 is prime
   ...Sexy prime with 37
   ...Twin prime with 29
   ...OEIS:002145 (4n+3; n=7)
   ...Super
   ...Right-truncatable
   31 is undulating
   31 is prime
   31 in octal is 037
   31 in hexadecimal is 0x1f
   31 in binary is 11111 (is odious)
   31 nearest square numbers: -6...5 (25...36 [6])
   sqrt(31) = 5.56776
   ln(31) = 3.43399
   log(31) = 1.49136
   31 reciprocal is .03225806451612903225806451612903
   31! is 8.22284e+33
   31 is 9.86761 Pi years
   31 is 1 score and 11 years
   31 written as a Roman numeral is XXXI

sqrt(31) ÷ ln(31) = 1.62137 which is the Golden Ratio (1.61803399) rounded the nearest hundredth.

[Wikipedia] "31, 331, 3331, 33331, 333331, 3333331, 33333331 are all prime. For a time it was thought that every number of the form 3_w 1 would be prime. However, the next nine numbers of the sequence are composite."

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 25 February 2009