|
| |
|
|
A064839
|
|
List the natural numbers starting a new row only with each new least prime signature (A025487). a(n) is the column position associated with n.
|
|
5
| |
|
|
1, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 1, 6, 3, 4, 1, 7, 2, 8, 3, 5, 6, 9, 1, 3, 7, 2, 4, 10, 1, 11, 1, 8, 9, 10, 1, 12, 11, 12, 2, 13, 2, 14, 5, 6, 13, 15, 1, 4, 7, 14, 8, 16, 3, 15, 4, 16, 17, 17, 1, 18, 18, 9, 1, 19, 3, 19, 10, 20, 4, 20, 1, 21, 21, 11, 12, 22, 5, 22, 2, 2, 23, 23, 2, 24, 25, 26
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,3
|
|
|
COMMENTS
| Row 2 records the primes (A000040). Rows 3 and 4 record the semiprimes (A001358). Rows 5, 6 and 9 record the 3-almost primes (A014612) etc. A058933 is a similar sequence based on k-almost primes.
The graph of this sequence is interesting for large n because it shows multiple curves, one for each prime signature. For example, the six highest curves on the graph of a(n) for n up to 10^4 are for the (1,1), (1,1,1), (1), (2,1,1), (2,1), and (1,1,1,1) prime signatures. The (1) curve dominates until n=58; the (1,1) curve dominates until n=1279786, when the (1,1,1) curve intersects the (1,1) curve. Each {1,1,...,1) curve dominates for a finite number of n.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
|
|
|
EXAMPLE
| The list begins as follows:
1
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 ...
4 9 25 49 ...
6 10 14 15 21 22 26 33 34 35 38 39 46 51 ...
8 27 ...
12 18 20 28 44 45 50 52 ...
16 ...
|
|
|
CROSSREFS
| A000040, A001358, A014612, A025487 and A058933.
Sequence in context: A028920 A055396 A057499 * A094741 A029234 A102613
Adjacent sequences: A064836 A064837 A064838 * A064840 A064841 A064842
|
|
|
KEYWORD
| easy,nice,nonn
|
|
|
AUTHOR
| Alford Arnold (Alford1940(AT)AOL.COM), Oct 24 2001
|
|
|
EXTENSIONS
| More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Oct 31 2001
|
| |
|
|
