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

1,1

Comments

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

Links

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

Example

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.

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

Prog

(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))

Crossrefs

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

Sequence in context: A202371 A195751 A072607 * A160828 A158129 A071319

Adjacent sequences: A306211 A306212 A306213 * A306215 A306216 A306217

Keyword

nonn

Author

Antonio Roldán, Jan 29 2019

Status

approved