13th generation
n. The generation born between 1961 and 1981, so-called because they are identified as the 13th generation since the founding of the United States.
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Examples
2004
For whatever reason, age labeling seemed to become a more prevalent and emotional issue with the advent of the concept of Gen X, aka twentysomethings, slackers, baby busters and the 13th Gen … as in the 13th generation since the founding of America.
—Cynthia McMullen, “Ageless, timeless?,” Richmond Times Dispatch (Richmond, Virginia), April 29, 2004
2003
"Generation X," for example, is now accepted almost universally to describe people born from the early '60s to around 1980 (the cutoff dates vary widely).

But that name, popularized by the title of a 1991 novel by Douglas Coupland, was rivaled for a while by such labels as "Baby Busters," a play on the baby boomers; the not exactly complimentary "Slackers"; and "13th Generation," based on the idea it is the 13th distinct age group since America was born.
—James Hebert, “Zoom goes the meaning of demographic term,” Copley News Service, November 10, 2003
1991 (earliest)
We label young Americans born between 1961 and 1981 the (Reactive) 13ers — partly because they are the 13th generation to know the U.S. flag, and also because of their lucklessness, the burden they feel from their "bad" reputation.
—William Strauss, “The 'Constellation' of 1991,” The Washington Post, February 24, 1991
Notes
This demographic label was coined by William Strauss and Neil Howe in their book Generations: The History of America's Future, 1584 to 2069. Here are their generations:
Awakening 1701-1723
Liberty 1724-1741
Republican 1742-1766
Compromise 1767-1791
Transcendental 1792-1821
Gilded 1822-1842
Progressive 1843-1859
Missionary 1860-1882
Lost 1883-1900
G.I. 1901-1924
Silent 1925-1942
Boom 1943-1960
Thirteenth 1961-1981
Millennial 1982-
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