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.