A279480 Numbers n such that n+1 and n^4+1 are primes.

1, 2, 4, 6, 16, 28, 46, 82, 88, 106, 180, 198, 210, 228, 238, 276, 312, 352, 430, 442, 466, 498, 540, 556, 568, 600, 616, 690, 732, 738, 742, 760, 768, 772, 786, 810, 856, 928, 936, 952, 966, 996, 1038, 1150, 1152

Offset: 1

Author

Ely Golden, Dec 12 2016

Keywords

• nonn

Comments

For any n > 1 in this sequence, (n+1)*(n^4+1) has the same nonzero digits as its prime factors in base n. - Ely Golden, Dec 12 2016

Links

• Ely Golden, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A070689 (the similar sequence for n+1 and n^2+1)

Programs

Mathematica

Select[Range@ 2000, Times @@ Boole@ Map[PrimeQ, {# + 1, #^4 + 1}] == 1 &] (* Michael De Vlieger, Dec 13 2016 *)
Select[Range[2000],AllTrue[1+{#,#^4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 13 2019 *)

PARI

list(lim)=my(v=List()); forprime(p=2,lim+1, if(isprime(1+(p-1)^4), listput(v, p-1))); Vec(v) \\ Charles R Greathouse IV, Dec 13 2016

SageMath

c=1
index=1
while(index<=1000):
    if((is_prime(c+1))&(is_prime(c**4+1))):
        print(str(index)+" "+str(c))
        index+=1
    c+=1
print("complete")

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Dec 13 2016