The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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