About the Number 1011001101 (one billion eleven million one thousand one hundred one)

When MathBabbler created a nBAB for the number 717 on 22 December 2011, he discovered that 717 when written in base-2 was the palindromic binary number 1011001101.

The MBNA (MathBabbler Number Analyst) encountered a couple of errors while processing the base-10 number 1011001101. Those errors were left in the MBNA output used in this nBAB.

   MathBabbler Number Analyst (MBNA) output:
   =========================================
   1011001101 is a natural, whole, integer
   1011001101 is odd
   1011001101 proper divisors are: 1,3,11,17,33,51,121,173,187,363,
                                   519,561,947,1903,2057,2841,2941,
                                   5709,6171,8823,10417,16099,20933,
                                   31251,32351,48297,62799,97053,114587,
                                   163831,177089,343761,355861,491493,
                                   531267,1067583,1802141,1947979,
                                   2785127,5406423,5843937,8355381,
                                   19823551,30636397,59470653,91909191,
                                   337000367,
   1011001101 is deficient (sum of divisors is 568579251)
   1011001101 is unhappy
   1011001101 is not a Harshad number
   1011001101 is not prime
   1011001101 has the prime factors: 3*11*11*17*173*947 (sum=1162)
   1011001101 sum of prime factors is: 1162
   1011001101 is palindromic
   ***error: input cannot exceed 100000
   1011001101 in octal is 07420523415
   1011001101 in hexadecimal is 0x3c42a70d
   1011001101 in binary is 111100010000101010011100001101 (is evil)
   1011001101 nearest square numbers: -15485...48108 
                                      (1010985616...1011049209 [31797])
   sqrt(1011001101) = 31796.2
   ln(1011001101) = 20.7342
   log(1011001101) = 9.00475
   1011001101 reciprocal is .00000000098911860631099352284483
   Runtime error: exponent too large in raise
   1011001101! is inf
   1.011e+09 is 3.21812e+08 Pi years
   1.011e+09 is 50550055 score and 1 year
   ./roman error:  number must be less that 4000
   1011001101 = 505500551^2 - 505500550^2  and
                505500551 + 505500550 = 1011001101

On 26 December 2011, when this was posted, 1011001101 was the the largest number having a nBAB.


Creator: Gerald Thurman [gthurman@gmail.com]
Created: 22 December 2011 (posted 26 December 2011)

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This work is licensed under a Creative Commons Attribution 3.0 United States License.