func Twins(a, b int) bool {
a_ := int64(a)
b_ := int64(b)
if isPrime[mathutil.FromDigits(append(mathutil.ToDigits(a_, 10),
mathutil.ToDigits(b_, 10)...), 10)] &&
isPrime[mathutil.FromDigits(append(mathutil.ToDigits(b_, 10),
mathutil.ToDigits(a_, 10)...), 10)] {
return true
}
return false
}
func Next(n int64) int64 {
factorialSum := int64(0)
for _, digit := range mathutil.ToDigits(n, 10) {
factorialSum += mathutil.Factorial(digit)
}
return factorialSum
}
// Return all the elements of the cartesian p-th power of Z_n
//
// For example, Z_3 = {0, 1, 2}, so (Z_3)**2 is the set of ordered pairs
// { (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), (2,2) }.
//
// The result has length n**power.
func CartesianPower(n int64, power int64) <-chan []int64 {
if power == 0 {
out := make(chan []int64, 0)
close(out)
return out
}
if n <= 0 {
panic("n must be positive")
}
if power <= 0 {
panic("power must be positive")
}
// Number of elements in the generated set
cardinality := int64(math.Pow(float64(n), float64(power)))
out := make(chan []int64)
go func() {
if n == 1 {
out <- make([]int64, power)
} else {
for i := int64(0); i < cardinality; i = i + 1 {
out <- sliceutil.ZeroPadLeftInt64(mathutil.ToDigits(i, n), power)
}
}
close(out)
}()
return out
}
func ConcatenatedProduct(integer, n int64) int64 {
digits := []int64{}
for i := int64(1); i <= n; i++ {
digits = append(digits, mathutil.ToDigits(integer*i, 10)...)
}
return mathutil.FromDigits(digits, 10)
}
func DigitSum(n int64) int64 {
return sliceutil.SumInt64(mathutil.ToDigits(n, 10))
}
func C(a, b int64) bool {
if isPrime[mathutil.FromDigits(append(mathutil.ToDigits(a, 10), mathutil.ToDigits(b, 10)...), 10)] && isPrime[mathutil.FromDigits(append(mathutil.ToDigits(b, 10), mathutil.ToDigits(a, 10)...), 10)] {
return true
}
return false
}