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<p>Automated edit (via create-page on MediaWiki MCP Server)</p> <p><b>New page</b></p><div>==Problem Statement==<br /> <br /> The arithmetic sequence, 1487, 4817, 8147, in which each of the terms increases by 3330, is unusual in two ways:<br /> * (i) each of the three terms is prime<br /> * (ii) each of the 4-digit numbers is a permutation of the same digits<br /> <br /> 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.<br /> <br /> What 12-digit number do you form by concatenating the three terms in this sequence?<br /> <br /> ==Approach==<br /> <br /> ===Generate 4-Digit Primes===<br /> <br /> Use a prime sieve to generate all primes up to 10,000. Discard primes below 1,000, leaving only the 4-digit primes.<br /> <br /> ===Group by Digit Permutations===<br /> <br /> For each 4-digit prime:<br /> * Convert the integer to a string<br /> * Sort its characters (digits) alphabetically<br /> * Use the sorted string as a key in a HashMap<br /> * Append the original prime to the list for that key<br /> <br /> After processing all primes, each entry in the map contains a group of primes that are digit permutations of one another.<br /> <br /> ===Find Arithmetic Sequences===<br /> <br /> For each group containing at least three members:<br /> * Sort the group in ascending order<br /> * Iterate over all pairs (a, b) within the group, where b &gt; a<br /> * Compute the third term: c = b + (b - a)<br /> * If c is also in the group, then (a, b, c) forms an arithmetic progression<br /> <br /> ===Exclude the Known Example===<br /> <br /> The problem statement gives 1487, 4817, 8147 as an example. Skip the sequence where a = 1487 so that only the other 4-digit sequence is reported.<br /> <br /> ===Return the Concatenation===<br /> <br /> Concatenate the three terms (a, b, c) as strings and return the resulting 12-digit number.<br /> <br /> ==Solution==<br /> <br /> Link: https://git.charlesreid1.com/cs/euler/src/branch/main/java/Problem049.java<br /> <br /> ==Flags==<br /> <br /> {{ProjectEulerFlag}}</div>

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