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A306214 Numbers that are the sum of fourth powers of three distinct positive integers in arithmetic progression.

%I A306214 #18 Feb 18 2019 02:14:53
%S A306214 98,353,707,962,1568,2177,2658,3107,4322,4737,5648,7187,7793,7938,
%T A306214 9587,11312,12657,13058,15392,15938,17123,19362,20657,23153,23603,
%U A306214 25088,28593,30963,31202,32738,34832,35747,40962,42528,45233,45377,49712,49763,54722,57153,57267,61250,63938,67667,69152
%N A306214 Numbers that are the sum of fourth powers of three distinct positive integers in arithmetic progression.
%C A306214 The remainder of a(n) divided by 16 is less than 5. - _Jinyuan Wang_, Feb 03 2019
%H A306214 Robert Israel, <a href="/A306214/b306214.txt">Table of n, a(n) for n = 1..10000</a>
%e A306214 353 = 2^4 + 3^4 + 4^4, with 3 - 2 = 4 - 3 = 1;
%e A306214 7187 = 1^4 + 5^4 + 9^4, with 5 - 1 = 9 - 5 = 4.
%p A306214 N:= 10^5: # for all terms <= N
%p A306214 Res:= NULL:
%p A306214 for a from 1 to floor((N/3)^(1/4)) do
%p A306214   for d from 1 do
%p A306214     v:= a^4 + (a+d)^4 + (a+2*d)^4;
%p A306214     if v > N then break fi;
%p A306214     Res:= Res, v
%p A306214   od
%p A306214 od:
%p A306214 sort(convert({Res},list)); # _Robert Israel_, Feb 17 2019
%o A306214 (PARI) for(n=1, 70000, k=(n/3)^(1/4); a=2; v=0; while(a<=k&&v==0, d=sqrt(sqrt(2*n+30*a^4)/2-3*a^2); if(d==truncate(d)&&d>=1&&d<=a-1, v=1; print1(n,", ")); a+=1))
%Y A306214 Cf. A000583, A126657, A133531, A190176, A306212, A306213.
%K A306214 nonn
%O A306214 1,1
%A A306214 _Antonio Roldán_, Jan 29 2019