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

Offset: 1

Author

Labos Elemer, Jan 21 2005

Keywords

• nonn

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)].

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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