The On-Line Encyclopedia of Integer Sequences (OEIS)

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A309763

Numbers that are the sum of 4 nonzero 4th powers in more than one way.
(history; published version)

#10 by Sean A. Irvine at Sat Jul 31 18:21:42 EDT 2021

STATUS

editing

approved

#9 by Sean A. Irvine at Sat Jul 31 18:19:28 EDT 2021

CROSSREFS

Cf. A000583, A003338, A018786, A025367, A025406, A309762, A344193, A344238, A344241, A344644.

STATUS

approved

editing

#8 by Bruno Berselli at Mon Oct 07 10:37:48 EDT 2019

STATUS

proposed

approved

#7 by Robert Israel at Mon Oct 07 10:23:06 EDT 2019

STATUS

editing

proposed

#6 by Robert Israel at Mon Oct 07 10:22:59 EDT 2019

LINKS

Robert Israel, <a href="/A309763/b309763.txt">Table of n, a(n) for n = 1..10000</a>

MAPLE

N:= 10^5: # for terms <= N

V:= Vector(N, datatype=integer[4]):

for a from 1 while a^4 <= N do

for b from 1 to a while a^4+b^4 <= N do

for c from 1 to b while a^4 + b^4+ c^4 <= N do

for d from 1 to c do

v:= a^4+b^4+c^4+d^4;

if v > N then break fi;

V[v]:= V[v]+1

od od od od:

select(i -> V[i]>1, [$1..N]); # Robert Israel, Oct 07 2019

STATUS

approved

editing

#5 by Susanna Cuyler at Thu Aug 15 21:34:58 EDT 2019

STATUS

proposed

approved

#4 by Ilya Gutkovskiy at Thu Aug 15 21:11:34 EDT 2019

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Thu Aug 15 19:44:19 EDT 2019

NAME

allocated for Ilya GutkovskiyNumbers that are the sum of 4 nonzero 4th powers in more than one way.

DATA

259, 2674, 2689, 2754, 2929, 3298, 3969, 4144, 4209, 5074, 6579, 6594, 6659, 6769, 6834, 7203, 7874, 8194, 8979, 9154, 9234, 10113, 10674, 11298, 12673, 12913, 13139, 14674, 14689, 14754, 16563, 16578, 16643, 16818, 17187, 17234, 17299, 17314, 17858, 18963, 19699

OFFSET

1,1

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BiquadraticNumber.html">Biquadratic Number</a>

EXAMPLE

259 = 1^4 + 1^4 + 1^4 + 4^4 = 2^4 + 3^4 + 3^4 + 3^4, so 259 is in the sequence.

MATHEMATICA

Select[Range@20000, Length@Select[PowersRepresentations[#, 4, 4], ! MemberQ[#, 0] &] > 1 &]

CROSSREFS

Cf. A000583, A003338, A018786, A025367, A025406, A309762.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Aug 15 2019

STATUS

approved

editing

#2 by Ilya Gutkovskiy at Thu Aug 15 19:44:19 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved