A237361
Numbers n of the form n = Phi_5(p) (for prime p) such that Phi_5(n) is also prime.
Original entry on oeis.org
4435770414505, 30562950873505, 32152890387805, 60700878873905, 936037312559305, 1279875801783805, 3780430049614405, 6055088920612205, 10370026462436905, 12160851727605005, 16956369914710105, 18746881534017005, 20813869508536105, 30740855019988405
Offset: 1
4435770414505 = 1451^4+1451^3+1451^2+1451+1 (1451 is prime), and 4435770414505^4+4435770414505^3+4435770414505^2+4435770414505+1 = 387147304469214558406348338836395337085545589397781 is prime. Thus, 4435770414505 is a member of this sequence.
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forprime(p=2,1e7, k=polcyclo(5,p) ; if( ispseudoprime(polcyclo(5,k)), print1(k", "))) \\ Charles R Greathouse IV, Feb 07 2014
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import sympy
from sympy import isprime
{print(n**4+n**3+n**2+n+1) for n in range(10**5) if isprime(n) and isprime((n**4+n**3+n**2+n+1)**4+(n**4+n**3+n**2+n+1)**3+(n**4+n**3+n**2+n+1)**2+(n**4+n**3+n**2+n+1)+1)}
A182384
Primes of the form k^5 + k^4 + k^3 + k^2 + k - 1.
Original entry on oeis.org
61, 37447, 111109, 271451, 1118479, 2000717, 5399041, 8308823, 17847787, 34636831, 133878821, 318877549, 790779659, 1475634067, 1705057969, 2924670137, 5337978007, 12284650663, 14830601147, 23073112417, 40380555731, 50414324357, 372777302329, 766855252057
Offset: 1
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Select[Table[n^5 + n^4 + n^3 + n^2 + n - 1, {n, 0, 300}], PrimeQ] (* T. D. Noe, Apr 27 2012 *)
A237445
Primes p such that f(f(p)) is prime, where f(x) = x^4 + x^3 + x^2 + x + 1 = A053699(x).
Original entry on oeis.org
1451, 2351, 2381, 2791, 5531, 5981, 7841, 8821, 10091, 10501, 11411, 11701, 12011, 13241, 15271, 15331, 16691, 17231, 18341, 18671, 19891, 20981, 21911, 23071, 23131, 23561, 23741, 24061, 25321, 27361, 29221, 30851, 30941, 31271, 32141, 33931
Offset: 1
1451 is prime and f(f(1451)) = 387147304469214558406348338836395337085545589397781 is prime. Thus, 1451 is a member of this sequence.
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f(x)=x^4+x^3+x^2+x+1;forprime(p=1,35000,ispseudoprime(f(f(p)))&&print1(p",")) \\ M. F. Hasler, Feb 09 2014
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import sympy
from sympy import isprime
{print(n) for n in range(10**5) if isprime(n) and isprime((n**4+n**3+n**2+n+1)**4+(n**4+n**3+n**2+n+1)**3+(n**4+n**3+n**2+n+1)**2+(n**4+n**3+n**2+n+1)+1)}
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