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?
#PrimeList #dig_split def p49 ps=[] p=PrimeList.new p.getNext while p.last<1000 ps.push(p.last) ps.push(p.getNext) while ps.last<10000 ps.pop categories=Hash.new([]) ps.each{|i|categories[dig_split(i).sort]+=[i]} categories.reject!{|k,v|v.length<3} categories.delete([1,4,7,8]) while(categories.size>1) categories.each_pair do |k,v| unless v[2]-v[1]==v[1]-v[0] if(v.length>3) v.shift else categories[k]=nil end end categories.reject!{|k,v|not v} end end puts categories.values.first.sort.join("") end