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.