# [seqfan] Re: A066077

rgwv at rgwv.com rgwv at rgwv.com
Thu Dec 28 02:46:15 CET 2017

```It should be noticed that the sequence is always increasing. The first difference of A066077 seems to be A066075.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of israel at math.ubc.ca
Sent: Wednesday, 27 December, 2017 7:15 PM
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Subject: [seqfan] A066077

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

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