A291654 Number of distinct values in the prime tree starting with n.

35, 35, 34, 22, 12, 11, 5, 7, 10, 5, 10, 10, 6, 6, 7, 7, 4, 3, 5, 13, 14, 6, 1, 5, 5, 3, 4, 3, 2, 2, 4, 3, 2, 2, 3, 3, 1, 4, 6, 3, 3, 3, 1, 3, 7, 6, 2, 2, 2, 6, 6, 1, 6, 9, 5, 5, 5, 2, 4, 5, 2, 2, 2, 7, 8, 7, 6, 2, 3, 4, 5, 3, 1, 1, 4, 5, 4, 4

Offset

1,1

Comments

Starting from n construct a tree that includes nodes for each prime in n^2 + n + 1, n^2 + n - 1, n^2 - n + 1, n^2 - n - 1, and recurse on each node until no further primes can be included.

Links

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

Ralf Steiner, Prime-trees, NMBRTHRY posting, 13 Aug 2017.

Example

a(5) = 12 since the tree for 5 looks like this where, for example, the symbol -[+-]->  stands for p^2+p-1 and the symbol -| stands for a leaf:
5-[--]->19-[+-]->379-[--]->143261-|
-[-+]->143263-[-+]->20524143907-|
-[+-]->29-[--]->811-|
-[++]->31-[--]->929-|
-[+-]->991-[-+]->981091-|

Maple

f:= proc(n) local  R, agenda;
  agenda:= {n}; R:= {n};
  while nops(agenda) > 0 do
    agenda:= select(isprime, map(t -> (t^2+t+1, t^2+t-1, t^2-t+1, t^2-t-1), agenda) minus R) ;
    R:= R union agenda;
  od;
  nops(R);
end proc:
map(f, [$1..100]); # Robert Israel, Aug 29 2017

Mathematica

f[n_] := Module[{R = {n}, agenda = {n}}, While[Length[agenda] > 0, agenda = Select[Flatten[Map[Function[t, {t^2 + t + 1, t^2 + t - 1, t^2 - t + 1, t^2 - t - 1}], agenda]] ~Complement~ R, PrimeQ]; R = Union[R, agenda]]; Length[R]];
Array[f, 100] (* Jean-François Alcover, Jul 30 2020, after Robert Israel *)

Crossrefs

Sequence in context: A022991 A023477 A307509 * A257948 A142728 A316111

Adjacent sequences: A291651 A291652 A291653 * A291655 A291656 A291657

Keyword

nonn

Author

Ralf Steiner and Sean A. Irvine, Aug 28 2017

Status

approved