[seqfan] A066077

israel at math.ubc.ca israel at math.ubc.ca
Thu Dec 28 01:15:21 CET 2017

```A066077 is "Smallest x such that p(n) = Sigma[x] - 1."
I don't know why the strange mix of [] and (), but
I would have assumed Sigma[x] is A000203(x) and p(n) is A000040(n), and the
Formula seems to confirm that.  But this doesn't match the Data at all.
The Data are

1, 2, 3, 4, 5, 7, 8, 10, 11, 14, 15, 17, 18, 21, 22, 25, 27, 30, 31, 32,
37, 38, 40, 43, 46, 48, 49, 51, 53, 54, 56, 58, 60, 61, 63, 64, 66, 67, 68,
74, 75, 79, 81, 86, 87, 88, 89, 90, 93, 96, 97, 100, 107, 108, 114, 115,
117, 120, 122, 123, 124, 125, 128, 130, 134, 135

and the values of A000203 corresponding to each of these are

1, 3, 4, 7, 6, 8, 15, 18, 12, 24, 24, 18, 39, 32, 36, 31, 40, 72, 32, 63,
38, 60, 90, 44, 72, 124, 57, 72, 54, 120, 120, 90, 168, 62, 104, 127, 144,
68, 126, 114, 124, 80, 121, 132, 120, 180, 90, 234, 128, 252, 98, 217, 108,
280, 240, 144, 182, 360, 186, 168, 224, 156, 255, 252, 204, 240

which seem to have no relation to prime(n)+1, except that they are never
equal!

The sequence that matches the definition would start

2, 3, 5, 7, 6, 13, 10, 19, 14, 29, 21, 37, 20, 43, 33, 34, 24, 61, 67, 30,
73, 57, 44, 40, 52, 101, 63, 85, 109, 74, 93, 86, 137, 76, 149, 111, 157,
163, 60, 173, 88, 117, 105, 193, 197, 199, 211, 84, 147, 229, 90, 114, 241,
96, 257, 215, 136, 201, 277, 281, 283, 164, 172, 126, 313, 317, 331, 337,
347, 349, 353, 120, 367, 373, 379, 186, 261, 397, 401, 409, 236, 421, 230,
208, 327, 365, 232, 457, 461, 463, 198, 168, 487, 326, 499, 204, 509, 346,
523, 541

and this seems not to be in OEIS.

So what's going on here?  What is A066077 really?

Cheers,
Robert
```