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

1,2

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

Formula

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

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 *)

Prog

(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")
(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

Crossrefs

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

Sequence in context: A162580 A098426 A365639 * A363785 A045665 A133492

Adjacent sequences: A279477 A279478 A279479 * A279481 A279482 A279483

Keyword

nonn

Author

Ely Golden, Dec 12 2016

Status

approved