A102642 a(n) = A102640(n) + A102641(n) - 1.

2, 3, 5, 5, 4, 5, 3, 4, 4, 5, 3, 7, 3, 6, 3, 3, 4, 6, 3, 6, 4, 7, 3, 6, 3, 5, 3, 5, 4, 7, 3, 5, 4, 5, 5, 7, 3, 6, 5, 5, 3, 6, 3, 6, 5, 5, 3, 7, 3, 5, 4, 5, 3, 6, 7, 3, 6, 3, 3, 4, 3, 5, 4, 3, 4, 6, 3, 5, 5, 6, 3, 7, 3, 5, 7, 5, 5, 6, 3, 5, 6, 5, 3, 4, 3, 5, 3, 6, 3, 5, 3, 5, 4, 5, 5, 5, 4, 6, 4, 7, 3, 6, 3, 4, 7

Offset: 1

Author

Labos Elemer, Jan 21 2005

Keywords

• nonn

Comments

A006530(2^n)=2 is a local minimum. Actual sequence displays the "width of valley" between the two nearest peaks of largest prime divisors. At the bottom of valley lies the number 2, the minimum.

Examples

			n=12: 2^10=4096. The greatest prime divisors of numbers around 4096 [both downward and upward] are as follows: {31, 4093, 89, 13, 2, 241, 683, 4099, 41}. The length of relevant sequence, i.e., between peaks 4093 and 4099 is 7, thus a(12)=7.
		

Crossrefs

Cf. A006530, A102640, A102641, A102643, A102644.

Programs

Mathematica

With[{nn = 12, lim = 105}, Map[Total@ # - 1 &, Transpose@ {Table[Function[k, 1 + LengthWhile[#, # > 0 &] &@ Differences@ Array[FactorInteger[#][[-1, 1]] &, nn, k]][2^n], {n, lim}], Table[Function[k, 1 + LengthWhile[#, # > 0 &] &@ Differences@ Table[FactorInteger[m][[-1, 1]], {m, k, k - nn, -1}]][2^n], {n, lim}]}]] (* Michael De Vlieger, Jul 30 2017 *)