A102644 A006530(x)=2 is a local minimum if x=2^n. Running downward with argument x started at 2^n, the largest prime divisor should increase. The value of first peak is a(n).

2, 3, 7, 13, 31, 61, 127, 127, 73, 1021, 89, 4093, 8191, 16381, 151, 257, 131071, 131071, 524287, 1048573, 337, 683, 178481, 16777213, 1801, 8191, 262657, 1877171, 2089, 46684427, 2147483647, 2147483647, 599479, 3360037, 6871947673, 283007

Offset

1,1

Comments

We may call these terms "downward-zenith-primes" belonging to 2^n-s. They do not exceed previous-primes before 2^n [A014234(n)].

Links

Michael De Vlieger, Table of n, a(n) for n = 1..150

Example

n=20: 2^20=1048576; the largest prime divisors for arguments if running downward from 2^20 are as follows: {2,41,524287,1048573,73}.
The first lower peak before argument 2^20=1048576 is a(20)=1048573.
n=1: a(1)=2 the peak equals the central value because there are no prime divisors>0 below n=2^1=2.

Mathematica

Table[2 + Total@ TakeWhile[Differences@ Map[FactorInteger[#][[-1, 1]] &,
TakeWhile[Range[2^n, 2^n - 20, -1], # > 0 &]], # > 0 &], {n, 36}] (* Michael De Vlieger, Jul 31 2017 *)

Crossrefs

Cf. A006530, A102640, A102641, A102642, A102643, A014234.

Sequence in context: A262829 A071899 A242389 * A014234 A124430 A002013

Adjacent sequences: A102641 A102642 A102643 * A102645 A102646 A102647

Keyword

nonn

Author

Labos Elemer, Jan 21 2005

Status

approved