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

1, 1, 1, 1, 1, 7, 38, 365

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: A356600 A354340 A229126 * A304012 A329528 A215441

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