In either a few weeks, or perhaps several years from now, Puerto Rico is set to become the 51st state, but if history (and the heart of congress) had gone differently, Puerto Rico would not be on it's way to becoming the 51st state. It would actually be on it's way to becoming either the 52nd or 53rd state of the Union.
Now there have been multiple proposals for new states over the years that never came to be. There have been several proposals for a state of Jefferson and a state of Lincoln (both in various sites). There have been proposals for the Upper Michigan peninsula to become it's own state, and even Long Island (along with New York City) to become it's own state. There was even a proposal for a state of Absaroka (which would have taken land from Northern Wyoming, South Eastern Montana, and Western South Dakota to form), but the two places that almost became their own states were called the states of Franklin and Sequoyah.
Now Franklin (if you could not tell was to be named after Benjamin Franklin) is part of what is now North Eastern Tennessee, but back when it attempted to become it's own individual state in 1785, it was actually apart of the state of North Carolina, because until 1796 Tennessee was apart of North Carolina.
Back in April 1784 North Carolina ceded what is today Tennessee to the Federal Government in order to pay off debts the state had gained as a result of the War of Independence. The government was reluctant to accept this, and also many frontiersmen in that region were pretty upset about this to, and also feared that the territory might even be sold to a foreign power, so in August of 1784 several counties in what is to North Eastern Tennessee seceded from North Carolina, which resulted in the state of North Carolina to rescind it's offer of cession, and even ordered judges to hold court in those counties, and send soldiers to the counties that wanted to secede. This of course did nothing to stop the growing secession movement, and on May 16, 1785 a delegation from the region submitted a petition to Congress for approval of statehood.
The State failed to receive the two-thirds majority of approval from the other states that is necessary in order to be admitted to the Union (only seven of the thirteen states at the time voted to admit Franklin to the Union) and couldn't even get the support of Benjamin Franklin himself.
In 1788 the region was finally disbanded and readmitted to North Carolina, and would later become part of Tennessee, but this would not be the last time the area would attempt to become it's own state, the most notable during the Civil War as a result of Eastern Tennessee disapproval of the rest of the state seceding from the union. While the region never did secede from the rest of Tennessee, there were many people there who proposed seceding from Tennessee and rejoining the Union (much like what West Virginia actually did when it seceded from Virginia and rejoined the Union in 1863).
Now as for the State of Sequoyah, which was to be named in honor of Sequoyah, a Cherokee silversmith who invented the Cherokee syllabary (or alphabet), the area which would have become it's own state was part of what is today Eastern Oklahoma, and was from 1890 until 1907 when it was merged with the Oklahoma Territory and became the State of Oklahoma, it's own individual territory known as the Indian Territory, which actually once included most of Oklahoma, but after 1890 a little over half the territory was ceded to white settlers to form it's own separate territory.
In 1905 the territory formed a constitutional convention, and voted to send a petition to the United States Congress for approval of statehood.
The delegation that arrived at Washington D.C. from the Indian Territories did not receive a warm reception, with many eastern politicians not wanting to admit two new western states. Even President Theodore Roosevelt proposed that the two territories be merged back again and become the State of Oklahoma (which is what happened in 1907). Still, all the hard work of the Sequoyah state constitutional convention was not lost as the Sequoyah constitution served as the basis for the Oklahoma constitution.
It should also be noted that if Sequoyah had ended up becoming a state, it would have been the first (and only) state where the majority of the people were Native Americans.