A158576 a(n) = number of components of the graph P(n,10) (defined in Comments).

1, 1, 1, 1, 1, 7, 38, 365, 3355, 33586

Offset: 1

Author

W. Edwin Clark, Mar 21 2009

Keywords

• base
• hard
• more
• nonn

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

Examples

			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. A050249, A145667, A145668, A145669, A145670, A145671, A145672, A145673, A145674, A158577, A158578, A158579, A253269.

Extensions

a(8) from W. Edwin Clark, Mar 31 2009

a(9)-a(10) from Max Alekseyev, Dec 23 2024