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p049.jl
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p049.jl
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#=
Prime permutations
Problem 49
The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the 4-digit numbers are permutations of one another.
There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property, but there is one other 4-digit increasing sequence.
What 12-digit number do you form by concatenating the three terms in this sequence?
=#
include("utils/primes.jl")
include("utils/permutations.jl")
ps = primes(1000,9999) # 4-digit primes
using Multisets
function perm_digs(n)
#permute the digits of n, return permuted integers in an array
sn = string(n)
arr = zeros(Int, length(sn))
for i=1:length(sn)
arr[i] = parse(Int, sn[i])
end
perms = permutations(arr)
return sort(parse.(Int, join.(perms)))
end
for i_p=1:length(ps)
p_perm = perm_digs(ps[i_p])
consider = p_perm[findall(isprime.(p_perm))] # find the permutations that are prime, nly need to consider these
c1 = ps[i_p]
for i_c2=1:length(consider) # using the fact the required sequences have three terms, could generalize
c2 = consider[i_c2]
d = c2 - c1 #difference
ds = consider .- c2
check = findall(ds .== d)
if length(check) >0
c3 = consider[check[1]]
if c1!=c2!=c3
println("$c1 $c2 $c3")
end
end
end
end
println("the three terms in the other 4-digit increasing sequence or primes that are permutations of each other, concatenate to the number 296962999629")