# Monthly Archives: September 2013

## Prime Num3ers p; DigitSum (p) = DigitSum (p^2)

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, … Continue reading

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## Prime numbers P such that P ± DigitProduct(P) is prime

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, … Continue reading

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## Num3ers of the form 10*x + y = (x^3 + y^3)/(x + y)

x^3  +  y^3 ———————-    =    10*x   +   y      x  +  y x^3  +  y^3 ———————-    =    100*x   +   y      x  +  y   (3^3   +   7^3) / … Continue reading

## Number 17328

The record for most Girl Scout cookie boxes sold by a single girl is 17328, set by Jennifer Sharpe at age 15. Mich. girl scout sells 17,328 boxes of cookies                                                    ——————————————   17328   has 30 divisors: 1 … Continue reading

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## Arithmetic Sequence | cube roots

In an Arithmetic Sequence the difference between one term and the next is a constant. If   a,   b,   c   form an arithmetic sequence, we can write a,           b = a + d,           c … Continue reading

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## Some musings on π — Part 4

3.141592653589793238462643383279502884197169399375105820974944592307816406286   Let’s form palindromes from the reflected pi digits and see how many primes we can produce: 3   is a prime number. 313   is a prime number. 31413   =   3 * 37 * 283 … Continue reading

## N/k is equal to the sum of the squares of digits of N

Solving the two equations (10*x   +   y)/k   =   x^2   +   y^2 (100*x   +   10*y   +   z)/k   =   x^2   +   y^2   +   z^2 for … Continue reading

## Num3er 513

513   is the concatenation of primes 5 and 13 513   =   5 || 13 513   has 8 divisors:     1,   3,   9,   19,   27,   57,   171,   513 Sum of … Continue reading