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

%I #25 Feb 13 2019 16:34:01

%S 1,16,95,334,877,12,3691,66,10649,16552,31,6,49285,66964,89027,2,

%T 149041,216,13823,22,93,20,30219,170,113,847576,988391,1146070,77733,

%U 948,11,1972066,131409,2522224,2836927,187038,3553741,3959260,4398539,286634,5385721,48,2351

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

%C From _Robert Israel_, Feb 13 2019: (Start)

%C a(n)+n-1 is the least divisor of (n-1)^4 + n^4 that is not less than n.

%C 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)

%H Robert Israel, <a href="/A066487/b066487.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) min(select(`>=`,numtheory:-divisors((n-1)^4+n^4),n))-n+1 end proc:

%p map(f, [$1..100]); # _Robert Israel_, Feb 13 2019

%t 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 *)

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

%Y Cf. A066333, A155211.

%K nonn,look

%O 1,2

%A _Benoit Cloitre_, Jan 02 2002

%E More terms from _Jean-François Alcover_, Feb 17 2018

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)