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A158576 a(n) = number of components of the graph P(n,10) (defined in Comments). 5
1, 1, 1, 1, 1, 7, 38, 365 (list; graph; refs; listen; history; text; internal format)



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]


Table of n, a(n) for n=1..8.


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).


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




W. Edwin Clark, Mar 21 2009


Added a(8) = 365. - W. Edwin Clark, Mar 31 2009



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Last modified October 2 17:06 EDT 2022. Contains 357227 sequences. (Running on oeis4.)