|
Search: id:A093489
|
|
|
| A093489 |
|
Define the total signature symmetry of a number n to be the number of values r takes so that n-r and n+r have the same prime signature. Sequence contains the total signature symmetry of n. |
|
+0
3
|
|
| 0, 0, 0, 1, 1, 1, 1, 3, 2, 3, 2, 4, 2, 3, 4, 5, 4, 7, 2, 6, 4, 5, 4, 10, 5, 5, 7, 7, 4, 10, 4, 10, 7, 7, 8, 16, 6, 7, 10, 11, 4, 14, 7, 10, 13, 9, 8, 18, 5, 13, 11, 12, 8, 20, 11, 17, 11, 13, 8, 27, 5, 10, 17, 16, 11, 19, 10, 14, 11, 15, 15, 33, 10, 15, 20, 15, 12, 23, 9, 22, 18, 13, 12, 31, 14
(list; graph; listen)
|
|
|
OFFSET
|
1,8
|
|
|
COMMENT
|
Number of partitions of 2n in two parts with identical prime signatures. Conjecture: (1) No term is zero for n > 3. (2) Every number k appears a finitely many times in the sequence. i.e. for every k there exists a number f(k) so that for all n > f(k), a(n) > k. Subsidiary sequence: the frequency of n.
|
|
EXAMPLE
|
a(12) = 4. The four values r can take are 1,2,5 and 7, giving the four pairs of numbers with identical prime signatures; (11,13),(10,14),(7,17) and (5,19).
|
|
CROSSREFS
|
Cf. A093488, A093491, A093492.
Sequence in context: A023509 A115041 A039641 this_sequence A066919 A084117 A116895
Adjacent sequences: A093486 A093487 A093488 this_sequence A093490 A093491 A093492
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 16 2004
|
|
EXTENSIONS
|
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jul 24 2006
|
|
|
Search completed in 0.002 seconds
|
