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A066487 a(n) = min( x : x^4 + n^4 = 0 mod (x+n-1) ). 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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 *)

PROG

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

CROSSREFS

Cf. A066333, A155211.

Sequence in context: A317150 A317608 A159245 * A318021 A320406 A241936

Adjacent sequences:  A066484 A066485 A066486 * A066488 A066489 A066490

KEYWORD

nonn,look

AUTHOR

Benoit Cloitre, Jan 02 2002

EXTENSIONS

More terms from Jean-François Alcover, Feb 17 2018

STATUS

approved

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)