Tag Archives: Beautiful Number

Num3er 1258723

    A Pentagonal number is a polygonal number of the form     is a prime number.     is also prime index of a 13-digital palindromic pentagonal number                     … Continue reading

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Num3er 135

    135   is composed of three digits in arithmetical progression 135   –   3   =   132       [3 being the middle digit] the digits of   135   will be reversed when, (132 * 3) … Continue reading

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Number 9182736455463728191

      Producing palindromes:   The pattern breaks:   The repeated digits in the middle are slowing diminishing:   These results show that only digits 1, 2, 4, 5, 7, 8 are repeated in the middle of each number. … Continue reading

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Numbers of the form 28(10^n – 1)

    Numbers of the form         is a palindrome whose square can be expressed as the product of two reversible numbers in two different ways:     It is the first palindromic integers containing just the … Continue reading

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Num3er 11296321

      is a perfect square containing precisely one 3, two 2’s and three 1’s. Any of the other seven digits   (0, 4, 5, 6, 7, 8, 9)   occur only once.     Find other examples.   … Continue reading

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Num3er 725

  Find an integer     which has 3 representations as a sum of 2 squares, such that, ,   and     are in arithmetic progression.   For example,     Paul found :           … Continue reading

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Prime number 593

                                           

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Num3er 122

    122   can be partitioned into two parts : the difference between   122   and the greatest square less than   122   gives us the first part the difference between the smallest square greater than   … Continue reading

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Num3er 7

      Next: Choose another integer n and using factorial, square root, floor and ceiling to obtain n Then, prove that this can be done for all n ≤ a large arbitrary number     E.g.       … Continue reading

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Num3er 952

      is the sum of the cubes of its digits plus the product of its digits:     Can you find other examples?   Paul found:                         … Continue reading

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