A155211 -id:A155211 - cp's OEIS frontend

A066487 a(n) = min( x : x^4 + n^4 = 0 mod (x+n-1) ).

1, 16, 95, 334, 877, 12, 3691, 66, 10649, 16552, 31, 6, 49285, 66964, 89027, 2, 149041, 216, 13823, 22, 93, 20, 30219, 170, 113, 847576, 988391, 1146070, 77733, 948, 11, 1972066, 131409, 2522224, 2836927, 187038, 3553741, 3959260, 4398539, 286634, 5385721, 48, 2351

Offset: 1

Benoit Cloitre, Jan 02 2002

From Robert Israel, Feb 13 2019: (Start)
a(n)+n-1 is the least divisor of (n-1)^4 + n^4 that is not less than n.
In particular, a(n) = (n-1)^4 + n^4 - n + 1 if (n-1)^4 + n^4 is prime, i.e. if n-1 is in A155211; otherwise a(n) <= ((n-1)^4 + n^4)/17 - n + 1 (because the least prime that can divide (n-1)^4 + n^4 is 17). (End)

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A066333, A155211.

f:= proc(n) min(select(`>=`,numtheory:-divisors((n-1)^4+n^4),n))-n+1 end proc:
map(f, [$1..100]); # Robert Israel, Feb 13 2019

a[n_] := For[x = 1, True, x++, If[Mod[x^4 + n^4, x + n - 1] == 0, Return[x]]]; Array[a, 30] (* Jean-François Alcover, Feb 17 2018 *)

a(n) = {my(k=1); while((k^4+n^4)%(k+n-1) != 0, k++); k; } \\ Altug Alkan, Feb 17 2018

More terms from Jean-François Alcover, Feb 17 2018

A241265 Numbers n such that n^4+(n+1)^4 is not prime.

Original entry on oeis.org

5, 7, 10, 11, 15, 17, 18, 19, 20, 21, 22, 23, 24, 28, 29, 30, 32, 35, 39, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 69, 70, 71, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 90, 91, 92, 93, 94, 95, 96, 99, 100, 101

Offset: 1

Vincenzo Librandi, Apr 20 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Complement of A155211.

[n: n in [1..200] | not IsPrime(n^4+(n+1)^4)];

Select[Range[200], ! PrimeQ[#^4 + (# + 1)^4] &]
Position[Total/@Partition[Range[120]^4,2,1],?CompositeQ]//Flatten (* _Harvey P. Dale, Mar 31 2024 *)

7 is in this sequence because 7^4+8^4 = 6497 = 73*89.

cp's OEIS Frontend

A066487 a(n) = min( x : x^4 + n^4 = 0 mod (x+n-1) ).

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