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

[Charles Greathouse]

>> Isn't that A014688?
> It seems to be. But I have not checked it out past the 50 terms stated.

It should hold for all terms, since A000040 is strictly monotonic (and
thus prime(n+1)+(n+1) - [prime(n)+n] >= 2).

So what do we do with A107820?

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Tue, Sep 6, 2011 at 9:34 AM, RGWv <rgwv at rgwv.com> wrote:
> Et al,
>
>   It seems to be. But I have not checked it out past the 50 terms stated.
>
>   As you can see, I constructed this sequence differently. I asked for the
> first number, a(n) which exceeded a(n-1) by at least 2 and such that a(n)-n
> was prime.
>
> Bob.
>
> -----Original Message----- From: Charles Greathouse
> Sent: Monday, September 05, 2011 11:44 PM
> To: Sequence Fanatics Discussion list
> Subject: [seqfan] Re: Slowest increasing sequence where a(n)-n is prime
>
> Isn't that A014688?
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Mon, Sep 5, 2011 at 5:48 PM, N. J. A. Sloane <njas at research.att.com>
> wrote:
>>
>> Bob, you said:
>>
>> Neil,
>>
>>   How about
>> {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.
>>
>>
>> Looks good! If no one else has a better suggestion, Bob,
>> would you go ahead and edit that sequence? Better wait until tomorrow,
>> just in case someone can recall the original discussion.
>>
>> Thanks
>>
>> Neil.
>>
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