[seqfan] Re: New formula for A030101 ?

[Marc LeBrun]

OK, I figured out that "Euler Problem" = "Euler Project Problem"

The first 99 values of f are

1 1 3 1 5 3 11 1 9 5 17 3 19 11 39 1 17 9 29 5 29 17 61 3 35 19 63 11 67 39
139 1 33 17 53 9 49 29 105 5 53 29 97 17 105 61 217 3 67 35 111 19 107 63
227 11 123 67 223 39 239 139 495 1 65 33 101 17 89 53 193 9 89 49 165 29 181
105 373 5 101 53 169 29 165 97 349 17 193 105 349 61 373 217 773 3 131 67
207

The related formula where instead the OTHER "-" is changed to a "+" gives

1 1 3 1 7 3 7 1 15 7 19 3 17 7 15 1 31 15 43 7 45 19 43 3 37 17 45 7 37 15
31 1 63 31 91 15 101 43 99 7 97 45 121 19 105 43 91 3 77 37 105 17 107 45
101 7 81 37 97 15 77 31 63 1 127 63 187 31 213 91 211 15 217 101 273 43 241
99 211 7 201 97 277 45 287 121 273 19 229 105 277 43 225 91 187 3 157 77 225

And changing BOTH "-"'s to "+"'s produces

1 1 3 1 7 3 11 1 15 7 23 3 25 11 39 1 31 15 47 7 53 23 83 3 53 25 81 11 89
39 139 1 63 31 95 15 109 47 171 7 113 53 173 23 189 83 295 3 109 53 165 25
187 81 293 11 189 89 289 39 317 139 495 1 127 63 191 31 221 95 347 15 233
109 357 47 389 171 607 7 233 113 353 53 399 173 625 23 401 189 613 83 673
295 1051 3 221 109 333

None of these seem to be in the OEIS.  I haven't tried superseeker.

Maybe there's some interesting connections, if anyone wants to go further.

--MLB