A093489 Define the total signature symmetry of a number n to be the number of values r takes such that n-r and n+r have the same prime signature. Sequence contains the total signature symmetry of n.

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

Offset

1,8

Comments

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) such that for all n > f(k), a(n) > k. Subsidiary sequence: the frequency of n.

Links

Charlie Neder, Table of n, a(n) for n = 1..1000

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: A115041 A039641 A198729 * A066919 A268714 A084117

Adjacent sequences: A093486 A093487 A093488 * A093490 A093491 A093492

Keyword

nonn,easy

Author

Amarnath Murthy, Apr 16 2004

Extensions

More terms from Joshua Zucker, Jul 24 2006

Status

approved