Mistake? A038853 and A038860

[Peter Pein]

Tanya Khovanova schrieb:
> Hello Seqfans,
> 
> Looking at the definitions, A038860 should be a subsequence of A038853; but 1385 is missing in A038853.
> 
> A038853  	 	 Numbers that are divisible by 5 and are differences between two cubes in at least one way.  
> 	215, 335, 485, 665, 875, 1115, 1330, 1685, 2015, 2170, 2375, 2680, 2765, 3150, 3185, 3635, 3880, 4095, 4115, 4570, 4625, 4905, 5165, 5320, 5735, 5805, 6130, 6335, 6795, 6965, 7000, 7625, 7875, 7930, 8315, 8920, 9035, 9045, 9260, 9785, 9970, 10305
> 
> A038860  	 	 Numbers n such that n ends with '5' and is difference between two cubes in at least one way.  
> 	215, 335, 485, 665, 875, 1115, 1385, 1685, 2015, 2375, 2765, 3185, 3635, 4095, 4115, 4625, 4905, 5165, 5735, 5805, 6335, 6795, 6965, 7625, 7875, 8315, 9035, 9045, 9785, 10305, 10565, 11375, 11655, 12215, 13085, 13095, 13985, 14625, 14915, 15875
> 
> Tanya
> 
> 
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> 
Hi seqfans,

"differences between two cubes in at least one way" leads to a start of
A038853 of:

35, 65, 125, 215, 250, 280, 335, 370,485, 520, 665, 730, 855, 875, 945,
 1000, 1115, 1125, 1330, 1385 ...


({#1, Reduce[{i^3 - j^3 == #1}, {i, j}, Integers, Backsubstitution -> True]} &
) /@
  {35, 65, 125, 215, 250, 280, 335, 370, 485, 520, 665, 730, 855, 875, 945,
   1000, 1115, 1125, 1330, 1385}

{{  35, (i == 2 && j == -3) || (i == 3 && j == -2)},
 {  65, (i == 1 && j == -4) || (i == 4 && j == -1)},
 { 125, (i == 0 && j == -5) || (i == 5 && j == 0)},
 { 215, (i == -1 && j == -6) || (i == 6 && j == 1)},
 { 250, i == 5 && j == -5},
 { 280, (i == 4 && j == -6) || (i == 6 && j == -4)},
 { 335, (i == -2 && j == -7) || (i == 7 && j == 2)},
 { 370, (i == 3 && j == -7) || (i == 7 && j == -3)},
 { 485, (i == -3 && j == -8) || (i == 8 && j == 3)},
 { 520, (i == 2 && j == -8) || (i == 8 && j == -2)},
 { 665, (i == -4 && j == -9) || (i == 9 && j == 4)},
 { 730, (i == 1 && j == -9) || (i == 9 && j == -1)},
 { 855, (i == 7 && j == -8) || (i == 8 && j == -7)},
 { 875, (i == -5 && j == -10) || (i == 10 && j == 5)},
 { 945, (i == 6 && j == -9) || (i == 9 && j == -6)},
 {1000, (i == 0 && j == -10) || (i == 10 && j == 0)},
 {1115, (i == -6 && j == -11) || (i == 11 && j == 6)},
 {1125, (i == 5 && j == -10) || (i == 10 && j == -5)},
 {1330, (i == -1 && j == -11) || (i == 11 && j == 1)},
 {1385, (i == -7 && j == -12) || (i == 12 && j == 7)}}

even if we use only positive cubes, A038853 is a mess. There is 1385 missing,
as Tanya noted and 1720 and 3250 are missing and for 3150 I dont't get the
difference of cubes.

Peter