A130790 Number of nodes in the Lucas-Pratt primality tree rooted at prime(n).

0, 1, 1, 2, 2, 2, 1, 2, 3, 3, 3, 2, 2, 4, 4, 3, 4, 3, 4, 4, 2, 4, 3, 3, 2, 2, 3, 4, 2, 3, 4, 4, 2, 5, 3, 3, 4, 2, 4, 5, 4, 3, 4, 2, 3, 4, 5, 4, 4, 4, 4, 4, 3, 2, 1, 5, 5, 3, 5, 4, 6, 3, 3, 5, 4, 5, 5, 4, 6, 5, 3, 5, 5, 5, 4, 5, 3, 4, 2, 3, 5, 5, 6, 2, 4, 4, 3, 4, 5, 6, 5, 5, 2, 4, 5, 3, 5, 4, 5, 3

Offset: 1

Author

R. J. Mathar, Jul 15 2007, Mar 07 2008

Keywords

• easy
• nonn

Comments

The primality tree starts at an odd prime at the root node. The branches of each node are the odd primes that divide the value of (the node minus 1). The length of the longest branch is related to A126805. Following the branch with the largest label gives A083647.

Links

• J. Bayless, The Lucas-Pratt primality tree, Math. Comp. vol 77 (2008) 495-502.

Crossrefs

Cf. A083647, A126805.

Cf. A037231 (primes which set a new record).

Programs

PARI

LP(p) = my(f=factor(p-1)); if(p <= 2, 0, 1+vecsum(vector(#f~, k, LP(f[k,1]))));
a(n) = LP(prime(n)); \\ Daniel Suteu, Nov 03 2019