Not expressible as x^3+-y^2

[Pfoertner, Hugo]

-----Ursprüngliche Nachricht-----
Von: Ralf Stephan [mailto:ralf at ark.in-berlin.de]
Gesendet am: 28 August, 2003 12:51
An: Pfoertner, Hugo
Cc: Sequence Fanatics
Betreff: Re: Not expressible as x^3+-y^2

> You wrote 
>> this one seems not to be in OEIS:
>> 6 14 16 21 27 29 32 34 42 46 51 58 59 62 66 69 70 75 77 78 84 85 86 88 90
...
>
>Nor is this (please submit too):
>
>Possible differences between a cube and the next smaller square.
>
>?
v=vector(200):for(n=2,10^7,t=n^3:s=sqrtint(t)^2:if(s==t,s=sqrtint(t-1)^2):
>tt=t-s:if(tt>0&&tt<=200&&!v[tt],v[tt]=n)):for(k=1,200,if(v[k],print1(k","))
)
>
>2,4,7,11,13,15,19,20,26,28,35,39,40,45,47,48,49,53,55,56,60,63,67,74,76,79,
81,83,100,104,107,109,
>116,127,135,139,146,147,148,150,152,155,170,174,180,184,186,191,193,200,

more terms
207,212,215,216,233,235,242,244,249,251,270,277,292,293,299,301,307,308,
343,355,362,364,366,368,371,391,405,424,431,433
>
> ralf

And the obvious inversion:

"Possible differences between a square and the next smaller cube"
seems to miss as well:
1 3 8 9 12 15 17 18 19 22 24 30 36 37 38 40 44 55 57 64 65 68 71 73 79 80
89 97 98 100 101 106 107 108 112 113 119 121 128 129 138 141 145 148 151
154 156 161 163 164 168 169 171 172 190 196 197 198 204 208 217 220 225
232 233 248 249 251 252 260 269 271 281 289 294 296 297 303 316 337 343

Some examples:
   2^2- 1^3= 3
   3^2- 2^3= 1
   4    2    8
   5    2   17
   6    3    9
   7    3   22
....
1138  109   15

Will be submitted next week.

Hugo