A179329 Number of iterations of (n + lpf(n)) / 2 required to reach a prime, where lpf equals the least prime factor.

0, 0, 1, 0, 2, 0, 1, 3, 3, 0, 1, 0, 2, 4, 4, 0, 4, 0, 1, 2, 2, 0, 1, 5, 3, 5, 5, 0, 5, 0, 1, 5, 5, 2, 1, 0, 2, 3, 3, 0, 3, 0, 1, 2, 2, 0, 6, 6, 4, 6, 6, 0, 6, 6, 1, 6, 6, 0, 1, 0, 2, 6, 6, 3, 6, 0, 3, 2, 2, 0, 1, 0, 3, 4, 4, 4, 4, 0, 1, 4, 4, 0, 1, 3, 2, 3, 3, 0, 3, 7, 1, 7, 7, 5, 7, 0, 5, 7, 7, 0, 7, 0, 1, 7, 7

Offset: 2

Author

Grant Garcia, Jan 12 2011

Keywords

• nonn

Comments

Zeros indicate prime indices.

Examples

			a(15) gives (15 + 3) / 2 = 9, (9 + 3) / 2 = 6, (6 + 2) / 2 = 4, (4 + 2) / 2 = 3. Four iterations were required to reach a prime, so a(15) = 4.
		

Crossrefs

Cf. A177980, A020639, A061228.

Programs

Mathematica

f[n_] := Length@ NestWhileList[(# + FactorInteger[#][[1, 1]])/2 &, n, ! PrimeQ@ # &] - 1; Array[f, 105, 2]