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

98, 353, 707, 962, 1568, 2177, 2658, 3107, 4322, 4737, 5648, 7187, 7793, 7938, 9587, 11312, 12657, 13058, 15392, 15938, 17123, 19362, 20657, 23153, 23603, 25088, 28593, 30963, 31202, 32738, 34832, 35747, 40962, 42528, 45233, 45377, 49712, 49763, 54722, 57153, 57267, 61250, 63938, 67667, 69152

Offset: 1

Author

Antonio Roldán, Jan 29 2019

Keywords

• nonn

Comments

The remainder of a(n) divided by 16 is less than 5. - Jinyuan Wang, Feb 03 2019

Examples

			353 = 2^4 + 3^4 + 4^4, with 3 - 2 = 4 - 3 = 1;
7187 = 1^4 + 5^4 + 9^4, with 5 - 1 = 9 - 5 = 4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000583, A126657, A133531, A190176, A306212, A306213.

Programs

Maple

N:= 10^5: # for all terms <= N
Res:= NULL:
for a from 1 to floor((N/3)^(1/4)) do
  for d from 1 do
    v:= a^4 + (a+d)^4 + (a+2*d)^4;
    if v > N then break fi;
    Res:= Res, v
  od
od:
sort(convert({Res},list)); # Robert Israel, Feb 17 2019

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))