|
Search: id:A062405
|
|
|
| A062405 |
|
Sums of specific numbers when generating a type of triangle based on pi(x). |
|
+0
1
|
|
| 2, 2, 5, 5, 8, 16, 11, 13, 18, 19, 20, 28, 30, 37, 30, 39, 39, 57, 46, 44, 52, 64, 62, 75, 60, 71, 79, 85, 74, 83, 90, 88, 95, 100, 111, 96, 104, 105, 115, 144, 117, 125, 148, 126, 132, 143, 165, 165, 144, 160, 172, 161, 174, 194, 173, 194, 198, 174, 212, 200, 205
(list; graph; listen)
|
|
|
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
|
Cf. A000040, A000720.
Sequence in context: A035624 A073707 A091609 this_sequence A071181 A079964 A103891
Adjacent sequences: A062402 A062403 A062404 this_sequence A062406 A062407 A062408
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Rory Kulz (entropix(AT)amnaria.com), Jul 08 2001
|
|
EXTENSIONS
|
More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Jun 27 2002
|
|
|
Search completed in 0.002 seconds
|
