A102327 Primes p such that the largest prime factor of p^5 + 1 is less than p.

1753, 2357, 7103, 9749, 13441, 16453, 21467, 22739, 25153, 28409, 29059, 33247, 33347, 36781, 42853, 51427, 57751, 58453, 62347, 65777, 66593, 69119, 72923, 78643, 80407, 83591, 85619, 89909, 91411, 99409, 101209, 101363, 113171, 124337

Offset

1,1

Links

Table of n, a(n) for n=1..34.

Formula

Solutions to {A006530(1 + p^5) < p} where p is a prime.

Example

p = 1753, 1 + p^5 = 16554252702583994 = 2*41*151*691*877*1361*1621, so the largest prime factor is 1621 < p = 1753.

Mathematica

<<NumberTheory`NumberTheoryFunctions` Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^5]] < # &] (* Ray Chandler, Jan 08 2005 *)
Select[Prime[Range[12000]], FactorInteger[#^5+1][[-1, 1]]<#&]  (* Harvey P. Dale, Mar 14 2011 *)

Prog

(PARI) isok(p)= isprime(p) && (vecmax(factor(p^5+1)[, 1]) < p); \\ Michel Marcus, Jul 11 2018

Crossrefs

Cf. A000040, A065091, A073501.

Sequence in context: A143994 A157325 A223448 * A076809 A272326 A271747

Adjacent sequences: A102324 A102325 A102326 * A102328 A102329 A102330

Keyword

nonn

Author

Labos Elemer, Jan 05 2005

Extensions

Extended by Ray Chandler, Jan 08 2005

Status

approved