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A306214 Numbers that are the sum of fourth powers of three distinct positive integers in arithmetic progression. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 23 03:00 EDT 2019. Contains 325230 sequences. (Running on oeis4.)