A158577 a(n) = size of the n-th term in S(10) (defined in Comments).

4, 21, 143, 1061, 8363, 68900, 1, 1, 1, 1, 1, 1, 586044, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5096511, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

W. Edwin Clark, Mar 21 2009

Keywords

• base
• hard
• nonn

Comments

Let H(L,b) be the Hamming graph whose vertices are the sequences of length L over the alphabet {0,1,...,b-1} with adjacency being defined by having Hamming distance 1. Let P(L,b) be the subgraph of H(L,b) induced by the set of vertices which are base b representations of primes with L digits (not allowing leading 0 digits). Let S(b) be the sequence of all components of the graphs P(L,b), L>0, sorted by the smallest prime in a component.

Next terms not equal 1: a(416) = 45082721 and a(3771) = 404171351 (see b-file). - Max Alekseyev, Dec 23 2024

Links

• Max Alekseyev, Table of n, a(n) for n = 1..37356

Crossrefs

Cf. A006879, A158576, A158578, A158579 (base 10).

Cf. A145667, A145668, A145669, A145670 (base 2).

Cf. A145671, A145672, A145673, A145674 (base 3).

Extensions

Terms a(51) onward from Max Alekseyev, Dec 23 2024