A102326 Primes p such that the largest prime divisor of p^4+1 is less than p.

10181, 14051, 18979, 25253, 57173, 58013, 60101, 62497, 65951, 66541, 69457, 75931, 82241, 82261, 84229, 87721, 88339, 88819, 91499, 92333, 95917, 99523, 105557, 107747, 109229, 118493, 118927, 137339, 146291, 155399, 157019

Offset

1,1

Comments

Primes in A309562. - Robert Israel, Aug 09 2019

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

p = 10181, 1+p^4 = 10743894862923122 = 2*17*1657*4657*5113*8009, so the largest prime factor is 8009 < p = 10181.

Maple

filter:= proc(p) max(numtheory:-factorset(p^4+1)) < p end proc:
select(filter, [seq(ithprime(i), i=1..20000)]); # Robert Israel, Aug 09 2019

Mathematica

<<NumberTheory`NumberTheoryFunctions` Select[Prime[Range[15000]], Max[PrimeFactorList[1 + #^4]] < # &] (* Ray Chandler, Jan 08 2005 *)
Select[Prime[Range[15000]], FactorInteger[#^4+1][[-1, 1]]<#&] (* Harvey P. Dale, Feb 27 2017 *)

Prog

(PARI) isok(p) = isprime(p) && (vecmax(factor(p^4+1)[, 1]) < p); \\ Michel Marcus, Jul 09 2018

Crossrefs

Cf. A000040, A065091, A073501, A309562.

Sequence in context: A184205 A128878 A050267 * A216262 A243410 A221119

Adjacent sequences: A102323 A102324 A102325 * A102327 A102328 A102329

Keyword

nonn

Author

Labos Elemer, Jan 05 2005

Extensions

Extended by Ray Chandler, Jan 08 2005

Status

approved