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A102643 A006530(x)=2 is a local minimum if x=2^n. Running upward with argument x, the largest prime divisor should increase. The value of first peak is a(n). 5
3, 5, 11, 17, 17, 13, 43, 257, 257, 41, 683, 4099, 2731, 2731, 331, 65537, 65537, 262147, 174763, 174763, 61681, 199729, 2796203, 2796203, 4051, 9586981, 87211, 15790321, 15790321, 1073741827, 715827883, 715827883, 6700417, 26317, 86171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We may call these terms "upward-zenith-primes" belonging to 2^n-s. They do not exceed next-primes after 2^n [A014210(n)].

LINKS

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

EXAMPLE

n=22: 2^22=4194304; largest prime divisors for n+j, j=0, 1, 2, ... are {2, 2113, 5419, 16981, 61681, 199729, 7109}. The first peak after 2^22=4194304 is a(22)=199729.

MATHEMATICA

Table[2 + Total@ TakeWhile[Differences@ Array[FactorInteger[#][[-1, 1]] &, 20, 2^n], # > 0 &], {n, 35}] (* Michael De Vlieger, Jul 31 2017 *)

CROSSREFS

Cf. A006530, A102640, A102641, A102642, A102644, A014210.

Sequence in context: A006169 A323582 A088328 * A279767 A125631 A045408

Adjacent sequences:  A102640 A102641 A102642 * A102644 A102645 A102646

KEYWORD

nonn

AUTHOR

Labos Elemer, Jan 21 2005

STATUS

approved

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Last modified May 20 04:41 EDT 2022. Contains 353851 sequences. (Running on oeis4.)