|
| |
|
|
A102326
|
|
Primes p such that the largest prime divisor of p^4+1 is less than p.
|
|
3
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
