Monthly Archives: January 2014

n consecutive integers / each integer has n distinct prime factors

  n  consecutive integers such that each integer has  n  distinct prime factors   n = 2 14   =   2   *   7 15   =   3   *   5 n = 3 644   … Continue reading

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Prime num3ers whose digit sum equals the number of digits

  For example,   Consider the prime numbers,  11,  1021, and  10103 : 11  is a 2-digit number                                             … Continue reading

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Sequence of (2^n – 1) consecutive integers all having n factors

  The Goal: To find a sequence of  (2^n – 1)  consecutive integers such that each of them has n prime factors   If   n = 2 The smallest sequence of  (2^2 – 1 = 3)  consecutive integers such that … Continue reading

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Num3er 1493

  1493  is the number of my followers on Twitter.     1493  is a prime number. 1493  is the sum of three consecutive primes: 1493  =  491  +  499  +  503 1493  =  2*15^2  +  2*15*7  +  17*7^2 1493  … Continue reading

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Fibonacci number | ceiling(√e^n) for n=0,1,…,8

  The first few Fibonacci numbers are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, … Continue reading

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Num3er 1490

  1490  is the number of my followers on Twitter     1490  has 8 divisors: 1    2    5    10    149    298    745    1490 1490   =   2  *  5  *  149 σ1(1490)   … Continue reading

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Num3er 1485

  1485  is the number of my followers on Twitter.     1485  has 16 divisors: 1   3   5   9   11   15   27   33   45   55   99   135   165 … Continue reading

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Fibonacci Num3ers and num3er of primes

  π(N) means the number of primes between 1 and N   Fibonacci Numbers N           π(N) ————————————————————————— 0                0                   … Continue reading

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Pattern | Fibonacci Num3ers- sum of square of digits is not 89

  The first few Fibonacci numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, … Continue reading

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Num3er 1488

  1488  is the number of my followers on Twitter.     1488  has 20 divisors: 1  2  3  4  6  8  12  16  24  31  48  62  93  124  186  248  372  496  744  1488 Sum of divisors: 3968 1488 … Continue reading

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