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 A291654 Number of distinct values in the prime tree starting with n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 12 18:11 EDT 2024. Contains 373359 sequences. (Running on oeis4.)