A066333 -id:A066333 - 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

A066486 a(n) = min( x : x^3 + n^3 == 0 mod (x+n-1) ).

Original entry on oeis.org

1, 6, 17, 34, 57, 2, 121, 6, 23, 262, 321, 386, 55, 534, 617, 88, 3, 902, 61, 144, 77, 52, 9, 1634, 1777, 1926, 17, 2242, 2409, 344, 2761, 198, 3137, 4, 3537, 164, 535, 4182, 4409, 112, 93, 5126, 5377, 768, 413, 6166, 453, 920, 7009, 7302, 1043, 22, 8217, 224, 13, 9186, 5, 34, 10209, 188, 19, 1560, 11657

Offset: 1

Benoit Cloitre, Jan 02 2002

nonn

Cf. A066333.

a[n_] := For[x = 1, True, x++, If[Mod[x^3 + n^3, x + n - 1] == 0, Return[x]]]; Array[a, 24] (* Jean-François Alcover, Feb 17 2018 *)

a(n) = {my(k=1); while((k^3+n^3)%(k+n-1) != 0, k++); k; } \\ Altug Alkan, Feb 17 2018

a(n) = 3*n^2 - 4*n + 2 for n=1, 2, 3, 4, 5, 7, 10, 11, 12, 14, 15, 18, 24, 25, 26, 28, 29, 31, 33, 35, 38, ...

That is, in those cases a(n) = A056109(n-1). It appears that the corresponding indices are given by A133431 (i.e., 1 U A002504). - Michel Marcus, Feb 17 2018

More terms from Altug Alkan, Feb 17 2018

cp's OEIS Frontend

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

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