A231813 Number of iterations of A046665(n) = (greatest prime divisor of n) - (least prime divisor of n) [with A046665(1) = 0] required to reach zero.

0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 3, 2, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 3, 3, 2, 1, 2, 1, 3, 2, 2, 2, 2, 1, 2, 1, 4, 1, 2, 3, 2, 3, 2, 1, 2, 3, 3, 3, 3, 3, 2, 1, 2, 2, 2, 1, 3, 1, 2, 2

Offset

0,7

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384 (terms 1..1000 from Clark Kimberling)

Antti Karttunen, Data supplement: n, a(n) computed for n = 0..100000

Formula

a(0) = 0; for n > 0, a(n) = 1 + a(A046665(n)). - Antti Karttunen, Jan 03 2019

Example

A046665(6) = 3 - 2, and A046665(1) = 0, so a(6) = 2.

Mathematica

z = 400; h[n_] := h[n] = FactorInteger[n][[-1, 1]] - FactorInteger[n][[1, 1]]; t[n_] := Drop[FixedPointList[h, n], -2]; Table[t[n], {n, 1, z}]; a = Table[Length[t[n]], {n, 1, z}]

Prog

(PARI)
A046665(n) = if(1==n, 0, my(f = factor(n), lpf = f[1, 1], gpf = f[#f~, 1]); (gpf-lpf));
A231813(n) = if(0==n, 0, 1+A231813(A046665(n))); \\ Antti Karttunen, Jan 03 2019

Crossrefs

Cf. A006530, A020639, A046665, A233510.

Sequence in context: A371883 A237353 A293460 * A158210 A322307 A087802

Adjacent sequences: A231810 A231811 A231812 * A231814 A231815 A231816

Keyword

nonn

Author

Clark Kimberling, Dec 11 2013

Extensions

Name edited, term a(0)=0 prepended and more terms added by Antti Karttunen, Jan 03 2019

Status

approved