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

Author

Benoit Cloitre, Jan 02 2002

Keywords

• nonn
• look

Comments

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)

Links

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

Crossrefs

Cf. A066333, A155211.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Extensions

More terms from Jean-François Alcover, Feb 17 2018