A188269
Prime numbers of the form k^4 + k^3 + 4*k^2 + 7*k + 5 = k^4 + (k+1)^3 + (k+2)^2.
Original entry on oeis.org
5, 59, 348077, 10023053, 30414227, 55367063, 72452489, 85856933, 109346759, 182679473, 254112143, 305966369, 433051637, 727914497, 2029672529, 4178961167, 6528621257, 8346080159, 12783893813, 17220494579, 17993776223, 19618171127, 23673478589, 29448235247, 43333033853
Offset: 1
5 is prime and appears in the sequence because 0^4 + 1^3 + 2^2 = 5.
59 is prime and appears in the sequence because 2^4 + 3^3 + 4^2 = 59.
348077 = 24^4 + (24+1)^3 + (24+2)^2 = 24^4 + 25^3 + 26^2.
10023053 = 56^4 + (56+1)^3 + (56+2)^2 = 56^4 + 57^3 + 58^2.
-
select(isprime, [n^4+(n+1)^3+(n+2)^2$n=0..1000])[]; # K. D. Bajpai, Apr 11 2014
-
lst={};Do[If[PrimeQ[p=n^4+n^3+4*n^2+7*n+5], AppendTo[lst, p]],{n,200}];lst
Select[Table[n^4+n^3+4n^2+7n+5,{n,500}],PrimeQ] (* Harvey P. Dale, Jun 19 2011 *)
-
for(n=1,1e3,if(isprime(k=n^4+n^3+4*n^2+7*n+5),print1(k", "))) \\ Charles R Greathouse IV, Jun 09 2011
A237364
Numbers n of the form n=Phi(7,p) (for prime p) such that Phi(7,n) is also prime.
Original entry on oeis.org
616067011, 58749951412747, 93054242152309543, 146945091162352770847, 2224989620406870255043, 43184085337135904888293, 53224134341571172990843, 109539169818149034933067, 308295173856880401026941, 6197901576526752380316343, 14789135287218506962379317
Offset: 1
616067011 = 29^6+29^5+29^4+29^3+29^2+29+1 (29 is prime) and 616067011^6+616067011^5+616067011^4+616067011^3+616067011^2+616067011+1 = 54672347801779330810964871392077416495507203132755717 is prime. Thus, 616067011 is a member of this sequence.
-
for k from 1 do
p := ithprime(k) ;
n := numtheory[cyclotomic](7,p) ;
pn := numtheory[cyclotomic](7,n) ;
if isprime( pn) then
print(n) ;
end if;
end do: # R. J. Mathar, Feb 07 2014
-
import sympy
from sympy import isprime
{print(n**6+n**5+n**4+n**3+n**2+n+1) for n in range(10**5) if isprime(n) and isprime((n**6+n**5+n**4+n**3+n**2+n+1)**6+(n**6+n**5+n**4+n**3+n**2+n+1)**5+(n**6+n**5+n**4+n**3+n**2+n+1)**4+(n**6+n**5+n**4+n**3+n**2+n+1)**3+(n**6+n**5+n**4+n**3+n**2+n+1)**2+(n**6+n**5+n**4+n**3+n**2+n+1)+1)}
A237446
Primes p such that f(f(p)) is prime where f(x) = Phi_6(x).
Original entry on oeis.org
29, 197, 673, 2297, 3613, 5923, 6133, 6917, 8219, 13553, 15667, 17137, 21911, 30941, 33587, 35407, 38053, 44017, 45557, 46663, 51241, 53453, 65731, 67187, 82349, 94151, 115361, 132287, 143711, 164011, 164291, 165523, 178613, 180797, 182141
Offset: 1
29 is prime and f(29^6+29^5+29^4+29^3+29^2+29+1) = 54672347801779330810964871392077416495507203132755717 is prime. Thus, 29 is a member of this sequence.
Comments