Euler 45

Studying the math, we learn that every hexagonal number is also triangular.

Therefore we only need to identify the next hexagonal number that is also pentagonal.

I have a helperfunction for that:

source("helpers.R")
is_pentagonal

## function(x){
##   if(x<1) return(FALSE)
##   s <- (sqrt(24*x +1)+1)/6
##   s == floor(s) # We probably need some way of controlling the precision
## }

Generate hexanogals, and continue until one is pentagonal. We can start at 144.

I also have a helper function for generating hexagonals:

hexagonal

## function(x){
##   2*x^2 - x
## }

found <- FALSE
n <- 144
while(!found){
  if(is_pentagonal(hexagonal(n))){
    answer <- hexagonal(n)
    found <- TRUE
  }else{
    n <- n + 1
  }
}