

A066487


a(n) = min( x : x^4 + n^4 = 0 mod (x+n1) ).


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
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OFFSET

1,2


COMMENTS

From Robert Israel, Feb 13 2019: (Start)
a(n)+n1 is the least divisor of (n1)^4 + n^4 that is not less than n.
In particular, a(n) = (n1)^4 + n^4  n + 1 if (n1)^4 + n^4 is prime, i.e. if n1 is in A155211; otherwise a(n) <= ((n1)^4 + n^4)/17  n + 1 (because the least prime that can divide (n1)^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((n1)^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] (* JeanFrançois Alcover, Feb 17 2018 *)


PROG

(PARI) a(n) = {my(k=1); while((k^4+n^4)%(k+n1) != 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 JeanFrançois Alcover, Feb 17 2018


STATUS

approved



