OFFSET
0,1
LINKS
Chris Caldwell, How Many Primes Are There?
FORMULA
pi(x) denotes the number of prime numbers less than or equal to x. Starting with x = 2 take pi(2x) - pi(x). The numbers 1, 1, 2, 1, 2, 2, 2, 3, 4, 3, ... will be found. Now create a new sequence based on the number of repeats. 2, 1, 1, 3, 1, 1, 1, ... Arrange these in a triangle such that 2 is the first row; 1, 1 is the second row; 3, 1, 1 is the third row; 1, 1, 2, 1 is the fourth row; etc. taking one more term each time. Now take the sum of the numbers on each row and this interesting sequence is generated.
EXAMPLE
Example: The first number on the triangle is 2 because the number 1 is repeated twice in the sequence of pi(2x) - pi(x).
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Rory Kulz (entropix(AT)amnaria.com), Jul 08 2001
EXTENSIONS
More terms from David Wasserman, Jun 27 2002
STATUS
approved