

A086320


a(n) is the depth of the prime tree formed when 4p + 3 is applied to the nth prime and repeatedly to any primes generated from the nth 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
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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*p3)), 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



