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

1,1

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.

Links

Table of n, a(n) for n=1..105.

Example

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).

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 *)

Crossrefs

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

Sequence in context: A113334 A127796 A131287 * A332581 A328059 A123674

Adjacent sequences: A102637 A102638 A102639 * A102641 A102642 A102643

Keyword

nonn

Author

Labos Elemer, Jan 21 2005

Status

approved