Sequence Challenge ANSWERS
The Virginia Mathematics Teacher   Fall 1984



Find the pattern and name the next three elements in the sequence.

1.       1, 2, 3, 5, 8, 13, 21, 34, ...
          Fibonacci Numbers

2.       3, 1, 4, 1, 5, 9, 2, 6, 5, ...
          Digits in the number Pi

3.       1, 3, 6, 10, 15, 21, 28, 36, 45, ...
          Triangular Numbers, or the sum
          of the first n natural numbers

4.       2, 3, 5, 7, 11, 13, 17, 19, 23, ...
          Primes

5.       1010, 1011, 1100, 1101, 1110,
          1111, 10000, 10001, 10010, ...
          Binary numbers beginning with 10

6.       1, 2, 6, 24, 120, 720, 5040,
          40320, 362880, ...
          Factorials

7.       1, 5, 14, 30, 55, 91, 140, 204,
          285, ...
          Square Pyramidal Numbers, or
          the sum of all the squares of the
          first n natural numbers

8.       1, 2, 10, 11, 12, 20, 21, 22, 100, ...
          Base three numbers

9.       1, 3, 7, 15, 31, 63, 127, 255,
          511, ...
          One less than a power of two

10.     2, 7, 1, 8, 2, 8, 1, 8, 2, ...
          Digits in the number e

11.     .01, .05, .1, .25, .5, 1, 2, 5, 10, ...
          Denominations of U.S. money
          system

12.     2, 3, 5, 6, 7, 8, 10, 11, 12, 13, ...
          Non-squares

13.     1, 4, 6, 8, 9, 10, 12, 14, 15, ...
          Non-primes

14.     1, 2, 2, 3, 2, 4, 2, 4, 3, 4 ...
          Number of integer divisors of
          natural numbers

15.     1, 4, 9, 61, 52, 63, 94, 46, 18, ...
          Reversals of the squares of
          the natural numbers

16.     12, 30, 24, 30, 36, 40, 42, 48,
          54, ...
          Abundant Numbers (those whose
          sum of proper divisors is greater
          than the number)

17.     15, 20, 20, 6, 6, 19, 19, 5, 14,
          20, ...
          Position in the alphabet of the first
          letter of the natural numbers

18.     12, 1, 1, 1, 2, 1, 3, 1, 4, ...
          The number of chimes of a
          grandfather's clock(that chimes
          on the half hour)

19.     12, 13, 14, 15, 20, 22, 30,
          110, 1100, ...
          Numbers for 12 in bases 10
          through 2

20.     1, 5, 12, 22, 35, 51, 70, 92, 117, ...
          Pentagonal numbers

21.     31, 59, 90, 120, 151, 181, 212,
          243, 273, ...
          Number of days in the year at
         the end of each month

22.     3, 3, 5, 4, 4, 3, 5, 5, 4, 3, ...
          The number of letters in the
          spelling of the natural numbers

23.     1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, ...
          The sum of the digits in the sum
          of the two previous numbers

24.     1, 4, 7, 11, 14, 17, 41, 44, 47,
          71, 74, ...
          Numbers written only with
          straight line segments

25.     11, 31, 71, 91, 32, 92, 13, 73,
          14, ...
          Reversal of the digits of the
          primes greater than ten

26.     8, 5, 4, 9, 1, 7, 6, 3, 2, 0, ...
          Alphabetical order of the names
          of our digits

27.     1, 8, 11, 69, 101, 181, 609, 619,
          689, 906, ...
          Numbers written with point
          symmetry

28.     4, 6, 8, 9, 10, 14, 16, 18, 19,
          20, 24, ...
          Numbers with closed loops

29.     14, 19, 29, 40, 44, 52, 59, 73,
          83, 94, ...
          Sum of the previous number and
          the sum of its digits beginning
          with the number 14

30.     1, 2, 6, 10, 4, 5, 9, 3, 7, 8, 11, ...
          The 3-letter, then 4-letter, then
          5-letter, etc., words for the
          natural numbers

Many thanks to Alice Mitchell for catching my error in the digits of pi.



Send any comments or questions to: David Pleacher