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

%I A279480 #14 Aug 13 2019 12:05:57
%S A279480 1,2,4,6,16,28,46,82,88,106,180,198,210,228,238,276,312,352,430,442,
%T A279480 466,498,540,556,568,600,616,690,732,738,742,760,768,772,786,810,856,
%U A279480 928,936,952,966,996,1038,1150,1152
%N A279480 Numbers n such that n+1 and n^4+1 are primes.
%C A279480 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
%H A279480 Ely Golden, <a href="/A279480/b279480.txt">Table of n, a(n) for n = 1..1000</a>
%F A279480 a(n) >> n log^2 n. - _Charles R Greathouse IV_, Dec 13 2016
%t A279480 Select[Range@ 2000, Times @@ Boole@ Map[PrimeQ, {# + 1, #^4 + 1}] == 1 &] (* _Michael De Vlieger_, Dec 13 2016 *)
%t A279480 Select[Range[2000],AllTrue[1+{#,#^4},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Aug 13 2019 *)
%o A279480 (SageMath)
%o A279480 c=1
%o A279480 index=1
%o A279480 while(index<=1000):
%o A279480     if((is_prime(c+1))&(is_prime(c**4+1))):
%o A279480         print(str(index)+" "+str(c))
%o A279480         index+=1
%o A279480     c+=1
%o A279480 print("complete")
%o A279480 (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
%Y A279480 Cf. A070689 (the similar sequence for n+1 and n^2+1)
%K A279480 nonn
%O A279480 1,2
%A A279480 _Ely Golden_, Dec 12 2016