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A086320 a(n) is the depth of the prime tree formed when 4p +- 3 is applied to the n-th prime and repeatedly to any primes generated from the n-th prime via this process. 1
11, 1, 6, 3, 10, 1, 3, 6, 5, 3, 2, 3, 2, 1, 9, 1, 6, 3, 3, 2, 1, 5, 1, 4, 1, 3, 2, 3, 4, 2, 1, 3, 1, 1, 3, 2, 3, 1, 1, 1, 5, 2, 8, 3, 1, 1, 1, 1, 2, 3, 5, 2, 2, 1, 3, 2, 1, 2, 1, 1, 4, 1, 2, 1, 4, 1, 5, 1, 1, 2, 3, 2, 3, 3, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 3, 1, 1, 4, 2, 1, 5, 4, 2, 1, 3, 1, 2, 2, 6, 4, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Note all prime trees have a minimum depth of 1, as the starting prime forms the root of the tree.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..65536

EXAMPLE

a(125) = 5 because the 125th prime is 691, which generates further primes through 4 repeated applications of 4p +- 3, giving a prime tree with generations as follows:

1. 691

2. 4 * 691 + 3 = 2767

3. 4 * 2767 + 3 = 11071

4. 4 * 11071 - 3 = 44281

5. 4 * 44281 + 3 = 177127

MAPLE

b:= proc(p) option remember;

      `if`(isprime(p), 1 + max(b(4*p+3), b(4*p-3)), 0)

    end:

a:= n-> b(ithprime(n)):

seq(a(n), n=1..120);  # Alois P. Heinz, Dec 02 2018

MATHEMATICA

f[n_] := f[n] = If[PrimeQ[n], 1 + Max[f[4 n - 3], f[4 n + 3]], 0]; f /@ Prime@Range@100 (* Amiram Eldar, Dec 02 2018 *)

CROSSREFS

Cf. A086319.

Sequence in context: A110305 A010199 A010200 * A185540 A095193 A171250

Adjacent sequences:  A086317 A086318 A086319 * A086321 A086322 A086323

KEYWORD

nonn

AUTHOR

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 17 2003

EXTENSIONS

Offset corrected by Alois P. Heinz, Dec 02 2018

STATUS

approved

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Last modified July 28 15:08 EDT 2021. Contains 346335 sequences. (Running on oeis4.)