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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). 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 26 13:24 EDT 2022. Contains 354883 sequences. (Running on oeis4.)