A379377 Consider the graph G whose vertices are pairs (i,x) (i >= 0) where the cyclotomic polynomial Phi_i(x) is prime, with edges connecting (i,x) to (i +- 1, x +- 1) if they are in the graph. a(n) is the number of vertices in the connected component of G containing (1,prime(i)+1).

5, 5, 5, 1, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 1, 4, 1, 1, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset

1,1

Comments

The first term > 5 is a(462028) = 8. Is the sequence bounded?

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 5 because prime(3) = 5 and the component of the graph containing (1,6) consists of the 5 vertices (1,6), (2,6), (3,5), (3,6) and (4,6).

Maple

f:= proc(n) local Agenda, S, count, t, dA;
      Agenda:= {[1, ithprime(n)+1]}; count:= 0; S:= {};
      while Agenda <> {} do
        t:= Agenda[1];
        Agenda:= subsop(1=NULL, Agenda);
        if isprime(numtheory:-cyclotomic(t[1], t[2])) and not member(t, S) then
         S:= S union {t}; count:= count+1;
         dA:= {[t[1]+1, t[2]], [t[1], t[2]+1]};
         if t[1] >= 1 then dA:= dA union {[t[1]-1, t[2]]} fi;
         if t[2] >= 1 then dA:= dA union {[t[1], t[2]-1]} fi;
         Agenda:= Agenda union (dA minus S);
        fi;
      od;
      count
end proc;
map(f, [$1..100]);

Crossrefs

Sequence in context: A374753 A230192 A172359 * A093796 A021647 A181668

Adjacent sequences: A379374 A379375 A379376 * A379378 A379379 A379380

Keyword

nonn

Author

Robert Israel, Dec 21 2024

Status

approved