A102640 Compute the greatest prime factors (GPFs, A006530()) of j + 2^n for j = 0, 1, ..., L. a(n) is the maximal length L of such a sequence in which the greatest prime factors are increasing with increasing j.

2, 2, 4, 2, 3, 2, 2, 2, 3, 2, 2, 4, 2, 3, 2, 2, 3, 4, 2, 3, 3, 6, 2, 3, 2, 4, 2, 2, 3, 4, 2, 3, 3, 2, 2, 4, 2, 4, 2, 2, 2, 4, 2, 3, 4, 4, 2, 4, 2, 3, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 3, 4, 2, 3, 4, 4, 2, 4, 2, 3, 2, 2, 4, 4, 2, 3, 3, 4, 2, 2, 2, 3, 2, 4, 2, 3, 2, 2, 3, 2, 2, 2, 3, 4, 2, 4, 2, 3, 2, 2, 3

Offset: 1

Author

Labos Elemer, Jan 21 2005

Keywords

• nonn

Comments

A006530(2^n)=2 is a local minimum. Going either upward or downward with the argument, the greatest prime factors are increasing for a while.

Examples

			For n = 12: 2^10 = 4096. The greatest prime factors of 4096, 4097, 4098, 4099 are as follows: {2, 241, 683, 4099}. A006530(4100) = 41 is already smaller than A006530(4099). Thus the length of increasing GPF sequence is 4 = a(12).
		

Crossrefs

Cf. A006530, A102641, A102642, A102643, A102644.

Programs

Mathematica

With[{nn = 12}, Table[Function[k, 1 + LengthWhile[#, # > 0 &] &@ Differences@ Array[FactorInteger[#][[-1, 1]] &, nn, k]][2^n], {n, 105}]] (* Michael De Vlieger, Jul 24 2017 *)