# [seqfan] Re: Slowest increasing sequence where a(n)-n is prime

RGWv rgwv at rgwv.com
Mon Sep 5 23:23:47 CEST 2011

```Neil,

{3, 5, 8, 11, 16, 19, 24, 27, 32, 39, 42, 49, 54, 57, 62, 69, 76, 79, 86,
91, 94, 101, 106, 113, 122, 127, 130, 135, 138, 143, 158, 163, 170, 173,
184, 187, 194, 201, 206, 213, 220, 223, 234, 237, 242, 245, 258, 271, 276,
279}
f[s_List] := Block[{k = 1, m = Last at s, n = Length@ s}, While[k < m + 2 || !
PrimeQ[k - n], k++]; Append[s, k]]; Rest@ Nest[f, {0}, 50]

Each term exceeds the previous term by at least 3.

Bob.

-----Original Message-----
From: N. J. A. Sloane
Sent: Monday, September 05, 2011 5:14 PM
To: seqfan at list.seqfan.eu
Cc: njas at research.att.com
Subject: [seqfan] Re: Slowest increasing sequence where a(n)-n is prime

Charles, about A107820: I've searched though my correspondence
from 2005, and I can't find any mention of that sequence, sorry.

I agree it doesn't make much sense. If you subtract n from the n-th
term this is what you get:

[2, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5,

5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
5, 5, 5, 5, 5, 5,

5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]

- which is not very satisfactory.

What if we required the primes we get to be distinct? Then I
suppose we will get some sequence already in the OEIS.

Neil

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```