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Math Trek

Sequence Puzzles

3:22pm, May 9, 2003

Given a sequence consisting of the whole numbers 1, 4, 9, 16, 25, 36, and 49, what number comes next in the sequence?

The most likely answer is 64–the next number in a sequence of squares of consecutive integers, starting with 1.

Such sequence puzzles are a staple of textbook exercises, brainteaser collections, and various intelligence and aptitude tests. Some sequences are easy to figure out, some have multiple interpretations, and others can require considerable head-scratching before the pattern becomes evident.

Neil A.J. Sloane of AT&T Shannon Labs in Florham Park, N.J., has been collecting number sequences ever since he was a graduate student at Cornell University in the 1960s. He described nearly 6,000 examples in his 1995 book The Encyclopedia of Integer Sequences and has added many thousands of additional examples to an online edition of the book (see

One useful feature of Sloane's onl

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