project euler – Problem 44

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Pentagonal numbers are generated by the formula, Pn=n(3n−1)/2. The first ten pentagonal numbers are:

1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...

It can be seen that P4 + P7 = 22 + 70 = 92 = P8. However, their difference, 70 − 22 = 48, is not pentagonal.

Find the pair of pentagonal numbers, Pj and Pk, for which their sum and difference is pentagonal and D = |Pk − Pj| is minimised; what is the value of D?

Calculate differences directly and test the differences to be pentagonal, if so test the sum to be pentagonal.
Use a while loop for have no idea the upper limit should be.

is.pent 

> system.time(source("Problem44.R"))
[1] 5482660
   user  system elapsed 
  12.64    0.00   12.67 

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