|
| |
|
|
A158576
|
|
a(n) = number of components of the graph P(n,10) (defined in Comments).
|
|
4
|
| |
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
Let H(n,b) be the Hamming graph whose vertices are the sequences of length n over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(n,b) be the subgraph of H(n,b) induced by the set of vertices which are base b representations of primes with n digits (not allowing leading 0 digits).
For 6 and 7 digit primes there is a single large component and the remaining components have size 1. For 8 digit primes there is a single large component, the size 2 component {89391959, 89591959} and the remaining components have size 1. [W. Edwin Clark, Mar 31 2009]
The elements of size 2 components in these graphs are sequence A253269. [Michael Kleber, May 04 2015]
|
|
|
LINKS
|
Table of n, a(n) for n=1..8.
|
|
|
EXAMPLE
|
The 6-digit primes 294001, 505447, 584141, 604171, 929573, 971767 (cf. A050249) have the property that changing any single digit always gives a composite number, so these are isolated nodes in the graph P(6,10) (which also has one large connected component).
|
|
|
CROSSREFS
|
Cf. A145667-A145674, A158577, A158578, A158579, A050249, A253269.
Sequence in context: A226200 A056197 A229126 * A304012 A215441 A027482
Adjacent sequences: A158573 A158574 A158575 * A158577 A158578 A158579
|
|
|
KEYWORD
|
base,hard,more,nonn
|
|
|
AUTHOR
|
W. Edwin Clark, Mar 21 2009
|
|
|
EXTENSIONS
|
Added a(8) = 365. - W. Edwin Clark, Mar 31 2009
|
|
|
STATUS
|
approved
|
| |
|
|
