A102643 - OEIS

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).

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

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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